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Ray Optics â?– Illustrative Examples 1) An object is placed at a distance of 6 cm from a convex mirror. If the focal length of mirror is 12 cm, find the position and nature of the image. Data : u = 6m; f = 12 cm; v = ?
(Ans. :
)
2) An object is placed at a distance of 6 cm from a concave mirror having radius of curvature 30 cm. Find the position and kind of the image. Data :
is negative.
(Ans. :
)
3) A convex surface separates two media of refractive indices 1.3 and 1.5. If the radius of curvature is 20 cm and an object is placed 260 cm from the refracting surface, calculate the distance of image from surface. Data :
(Ans. :
)
4) An object is placed at a distance of 25 cm from a convex lens of focal length l0 cm. Determine the position of image. Data : u = - 25 cm, f = 10 cm, v = ?
(Ans. : Thus, v = 16.7 cm)
5) A plano-convex lens has a focal length of 60 cm. If the refractive index of the material is 1.5, find its radius of curvature. Data :
(Ans. :
)
6) Determine the focal length of a bi-convex lens of radii of curvatures 30 cm and 40 cm. What will be its focal length if the lens is immersed in water? Data : R1 = + 30 cm, R2 = - 40 cm
(Ans. :
)
7) In a optical system, two thin convex lenses used are in contact. If the focal lengths of them are l5 cm and l0 cm, find the effective focal length of the system. Data :
(Ans. : f = 6 cm.)
8) A convex lens of focal length 4.0 cm is used as simple microscope. Find its magnifying power when (i) image is at infinity and
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(ii) image at DDV. Data : f = 4.0 cm.
(Ans. :
)
9) For a compound microscope the focal lengths of objective and eyepiece are 3.0 un and 5.0 cm respectively. A small object is placed at 4.0 cm from the objective. Find the magnifying power, if the final image is formed at DDV. Data :
(Ans. : 10)
)
A telescope has an objective of focal length 200 cm and an eyepiece of focal length 8 cm. Find the magnifying power and the length of telescope. Data :
(Ans : MP = -25, Length of telescope L = 208m)
â?– Theory Questions 1)
For a spherical mirror system, define (a) principal axis, (b) optical centre. (c) radius of curvature. (d) pole, (e) focal point.
2)
State the New Cartesian Sign Convention used in optics.
3)
Obtain the mirror equation for spherical mirror system.
4)
Explain refraction at single curved surface (convex) and obtain relation among u, v and R.
5)
Derive the lens maker’s equation and deduce the lens formula from it.
6)
Explain the concept of conjugate foci.
7)
Discuss the system, which uses two thin convex lenses in contact.
8)
Define M.P. of simple microscope and M.P. of telescope.
9)
What is simple microscope? Obtain the expression for its magnifying power.
10)
Draw a neat labelled ray diagram for compound microscope and obtain the expression for its magnifying power.
11)
Draw a neat labelled ray diagram for refracting telescope. Obtain the formula for its magnifying power.
12)
Why do the objects to be viewed through a compound microscope must be brightly illuminated?
13)
Why do telescopes have large sized objective?
14)
Draw the schematic diagram of reflecting telescope and explain its working.
15)
Define ray optics.
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Define the following terms. i. Ray of light
ii. Beam of light
17)
State laws of reflection of light.
18)
What is spherical mirror? State different types of spherical mirror.
19)
Define the following terms in case of a spherical mirror: i. Pole ii. Principal axis iii. Centre of curvature iv. Radius of curvature v. Principal focus or focal point vi. Focal length vii. Aperture
20)
Define: i. Concave mirror
21)
ii. Convex mirror
State the relation between focal length and radius of curvature of a spherical mirror.
22)
State the nature of image in a concave mirror and convex mirror for various positions of object.
23)
Can a virtual image be photographed by camera?
24)
Define lens. Explain different types of lenses.
25)
Define the following terms for a curved lens. i. Optical centre ii. Principal focus iii. Focal length iv. Centre of curvature v. Radius of curvature vi. Principal axis vii. Aperture viii. Principal section
26)
If a thin lens is dipped in water, will its focal length change?
27)
What is myopia? How can it be corrected?
28)
What is hypermetropia? How can it be corrected?
29)
Explain the following terms. i. Visual angle ii. Distance of distinct vision iii. Power of accomodation
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iv. Power of lens 30)
A. What is compound microscope? B. Describe the construction and working of a compound microscope with a neat ray diagram. Also state its uses.
31)
Explain the need of compound microscope.
32)
Distinguish between magnification and magnifying power.
33)
Distinguish between simple microscope and compound microscope.
34)
Answer the following questions: A. You have learnt that plane and convex mirrors produce virtual images of j objects. Can they produce real images under some circumstances? Explain. B. A virtual image, we always say, cannot be caught on a screen. Yet when we see j a virtual image, we bring it to the j screen i.e. retina of our eye. Is there a j contradiction?
35)
What is a telescope? State different types of telescopes.
36)
Obtain an expression for the magnifying power of astronomical telescope, if final image is formed at distance of distinct vision.
37)
Suppose the upper half of a convex lens is painted black. What change is produced in the real image formed by the lens?
38)
What are the problems or limitations or drawbacks of refracting telescope?
39)
How can we overcome drawbacks of refracting telescope?
40)
Distinguish between refracting telescope and reflecting telescope.
â?– Textbook Problems 1) A convex lens has focal length 20 cm, which produces an image four times larger than object. Calculate the possible positions of objects. [Hint : MP = D/u v/u] (Ans : -25cm, -15cm) 2) A plano-convex lens of glass has radius of curvature of 30 cm. If the glass has refractive index of 1.6, find the focal length of lens.
(Ans : +50 cm)
3) A convex lens used as simple microscope has focal length of 2.5 cm. Find its magnifying power for the image at DDV and the position of the object. (Ans : 11, - 2.27 cm) 4) A compound microscope has an objective and eyepiece of focal lengths 2.5 cm and 6.0 cm respectively. The lenses are 20 cm apart. A small object is kept at 3 cm from the objective. Find the distance of final image from eyepiece and the magnifying power of microscope.
(Ans : 30 cm, 30)
5) The objective and eyepiece of an astronomical telescope are 60 cm apart. If the magnifying power of telescope is 19, find the focal lengths of both the lenses.
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6) A compound microscope has a magnifying power of 40. Assume that the final image is formed at DDV. If the focal length of eyepiece is l0 cm, calculate the magnification produced by objective.
(Ans : 11.4)
7) A conve.t lens has total length of 2.0 cm. Find its magnifying power if image is formed at DDV.
(Ans : 13.5)
8) A glass slab has concave surface of radius of curvature 2.0 cm. The glass has refractive index of 1.5. If a point object is placed on axis in air at a distance of 18 cm from concave face, find the position and nature of the image. (Ans : -4.9cm, virtual) 9) An objective is placed at 15 cm from a convex mirror having the radius of curvature 20 cm. Find the position and kind of image formed by it. (Ans: + 6 cm, virtual, erect) 10)
An optical system uses two thin convex lenses in contact having the effective focal length of
cm. If one lens has focal length of 30 cm, find the focal length of the
other lens.
(Ans : 10 cm)
❖ Practice Problems ➢ Type-I : problems based on mirror equation 1) A concave mirror has radius of curvature of 40 cm. An object is placed at a distance of 16 cm from it. Find the position and nature of the image formed by it. (Ans : 80 cm) 2) A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.
(Ans : 0.56)
3) A convex mirror has focal length of 10 cm. An object is placed at a distance of 15 cm from it. Find the position and nature of the image formed by it. (Ans : 6 cm, virtual, erect, behind the mirror.) 4) An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. Find the position and nature of the image formed by it. (Ans : 24 cm, real, inverted, same side as that of object or infront of the mirror.) 5) An object is placed at a distance of 5 cm from a concave mirror of focal length 15 cm. Find position and nature of the image formed by it. (Ans : 7.5 cm, virtual, erect, behind the mirror)
➢ Type-II : Problems based on refraction through thin curved surface
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6) An object is placed infront of a convex surface separating two media of refractive index 1.1 and 1.5. The radius of curvature is 40 cm. Where is the image formed when an object is placed at 220 cm from the refracting surface?
(Ans : 300 cm.)
7) There is an air bubble inside a glass sphere of radius 5 cm. The bubble appears 2 cm below the outer surface when looked at, in the line of the diameter containing the bubble. Find the actual position of the bubble. The refractive index of glass being 1.5.
(Ans : 2.5 cm.)
8) Light from a point source in air falls on a convex spherical glass surface (
,
radius of curvature = 20 cm). The distance of light source from the glass surface is 100 cm. At what position is the image formed?
(Ans : + 100 cm)
9) What curvature must be given to the bounding surface of an object in the medium of
for virtual image of
at 10 cm to be formed at a distance of 40 cm. (Ans : 8 cm)
➢ Type-III : Problems based on Lens makers’ equation 10)
Double-convex lenses are to be manufactured from a glass of refractive index 1.55, with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be 20 cm?
11)
(Ans : 22 cm.)
A convex lens has focal length of 0.15 m. At what distance an object should be placed from the lens, so as to obtain an image whose size is three times the size of the object?
12)
(Ans : 20 cm or 10 cm)
An object of size 3.0 cm is placed 14 cm in front of a concave lens of focal length 21 cm. Describe the image produced by the lens. What happens if the objects is moved further away from the lens?
(Ans : i. The image is virtual, erect and diminished and is formed on the same side of the lens at a distance of 8.4 cm from the lens and has a height of 1.8 cm. ii. If the object is moved away from the lens, the image moves towards the principal focus and goes on diminishing in size.) 13)
The radii of curvatures of the two surfaces of a convex lens are 12 cm and 18 cm. If the focal length of the lens is 14.4 cm, find
14)
.
(Ans : 1.5)
Calculate the focal power of a concave lens of
with radii of curvature 30 cm
and 15 cm.
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(Ans : 5)
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The radii of curvature of the faces of a double convex lens are 10 cm and 15 cm. If focal length is 12 cm, what is the refractive index of glass?
16)
(Ans : 1.5)
Determine the focal length of bi-convex lens of radii of curvatures 12 cm and 18 cm. What will be its focal length if the lens is immersed in water? (Ans : 14.4 cm in air, 57.6 cm in water)
17)
A convex lens has radii of curvatures 30 cm and 40 cm respectively. The lens is made up of glass of R.I. 1.5. Find the focal length and position of the image when an object is placed at 42 cm from it.
18)
(Ans : 34.3 cm, 186.6 cm)
A plano-convex lens has the radius of curvature of its spherical surface 25 cm. If the refractive index of the material of lens is 1.5, find the focal length of the lens. (Ans : 50 cm)
➢ Type-IV : Problems based on magnifying power of simple microscope 19)
What must be the focal length of a lens used as simple microscope of magnifying power 26? The final image is formed at the distance of distinct vision. (Ans : 1 cm)
20)
A simple microscope has a magnifying power 5 when the image is formed at the distance of distinct vision (25 cm). Find its focal length.
21)
(Ans : 6.25)
Calculate the magnifying power of a convex lens of focal length 2 cm when the image is formed at the distance of distinct vision.
22)
(Ans : 13.5)
An object is placed at a distance of 4.5 cm from a simple microscope of focal length 5 cm. Find the magnification and magnifying power in this case. The distance of distinct vision is 25 cm.
(Ans : 10, 6)
➢ Type-V : Problems based on magnifying power of compound microscope 23)
A compound microscope has a magnification of 15. If the object subtends an angle of 0.5° to eye, what will be the angle subtended by the image at the eye? (Ans : 7.5°.)
24)
A compound microscope has an objective of focal length 2 cm and an eye piece of focal length 5 cm. An object has to be placed at a distance of 1.2 cm away from the objective for normal adjustment. Find the angular magnification and length of the microscope tube.
25)
(Ans : i. 16.65 ii. 8.33 cm)
In a compound microscope, the focal lengths of the objective and the eye-piece are 1.25 cm and 5 cm respectively. An object is kept at a distance of 1.5 cm from the objective. If the final image is formed at D, what is the M.P.?
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➢ Type-VI : Problems based on magnifying power of astronomical telescope 26)
Magnifying power of an astronomical telescope is 12 and the image is formed at D.D.V. If the focal length of the objective is 90 cm, what is the focal length of the eyepiece?
27)
(Ans : 5.7 cm.)
A small telescope has an objective lens of focal length 140 cm and an eye-piece of focal length 5.0 cm. What is the magnifying power of the telescope for viewing distant objects when i. the telescope is in normal adjustment (i.e. when the final image is at infinity)? ii. the final image is formed at the least distance of distinct vision (25 cm)? (Ans : (i) 28 (ii) 33.6)
28)
Two convex lenses of an astronomical telescope have focal length 1.3 m and 0.05 m respectively. Find the magnifying power and the length of the telescope.
(Ans : i. Magnifying power of the telescope is 26. ii. Length of the telescope is 1.35 m.) 29)
An astronomical telescope consists of two thin lenses set 36 cm apart and has a magnifying power 8. Calculate the focal length of the lenses. (Ans: Focal length of objective lens is 32 cm and that of eyepiece is 4 cm.)
30)
An astronomical telescope has an eyepiece of focal length of 0.05 m. If the length of the telescope is 4.05 m, find the magnification produced in the normal adjustment. (Ans : 80)
31)
A Galilean telescope is 27 cm long when focussed to form the image at infinity. If the objective has a focal length of 30 cm, what is the focal length of the eyepiece? (Ans : 3 cm)
32)
A telescope has an objective of focal length 25 cm and an eye-piece of focal length 5 cm both lenses being convex. What is its M.P. when the final image is formed at the distance of distinct vision and at infinity ?
33)
(Ans : 6, 5)
An astronomical telescope has an objective of focal power 1 diopter and an eyepiece of focal power 25 diopter. What is the distance between the lenses for normal adjustment of telescope? What is the M.P. then?
(Ans : 104 cm, 25)
➢ Type-VII: Miscellaneous
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An object is placed in front of a convex mirror at a distance of 25 cm from it. If the focal length of convex mirror is 6.25 cm, find the position and nature of the image. (Ans : 5 cm)
35)
What is the focal length of a combination of a convex lens of focal length 30 cm and a concave lens of focal length 20 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses. (Ans : i. The focal length of the combination is 60 cm. ii. Since the focal length is negative, the combination is a diverging lens.)
36)
A double convex lens is made up of the material of refractive index 1.5 and its radii of curvature are 15 cm and 30 cm respectively. Find its focal length, if it is surrounded by the material of refractive index 1.07.
37)
(Ans : 25 cm)
Calculate the magnifying power of a magnifying glass of 5 cm focal length, when image is at D.D.V. [D.D.V = 25 cm]
38)
(Ans : 6)
A compound microscope has an objective of focal length 1 cm and an eye-piece of focal length 2.5 cm. An object is situated at a distance of 1.5 cm from the objective. What is the magnifying power of the microscope when the final image is i. at infinity? ii. at the distance of distinct vision (25 cm)? (Ans : i. The magnifying power of the compound microscope when the final image is formed at infinity is 210. ii. Its magnifying power when the final image is formed at D.D.V. is 231.)
39)
An object is placed at the centre of hollow sphere. The inner and outer radii of the surface of the hollow sphere are 8 cm and 9 cm. Where will the image be formed when looked at from outside?
40)
A symmetrical double concave glass lens has a focal length of 25 cm. What is the radius of curvature of each of its two surfaces?
41)
(Ans : Image is formed at centre)
(Ans : 22 cm)
The focal length of a magnifying glass is 10 cm. If a person whose least distance of distinct vision is 25 cm, uses the glass, find the maximum magnification possible. (Ans : 3.5)
42)
A biconvex lens of focal length 20 cm has radius of curvatures 20 cm and 30 cm. Determine the R.I. of material of lens.
43)
(Ans : 1.6)
The radius of curvature of either face of a double convex lens is equal to its focal length. Find the R.I. of the material of the lens.
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(Ans : 1.5)
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A convex lens of focal length 15 cm in air is immersed in water. Find its focal length in water.
45)
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and for glass
.
(Ans : 60 cm)
An object is placed infront of a convex mirror of focal length 20 cm at a distance of 16 cm from it. Find the position and nature of the image formed by it. (Ans : 8.9 cm, virtual, erect, behind the mirror)
â?– Multiple Choice Questions 1) A converging lens may not have (A) a positive focal length.
(C) one plane surface.
(B) a negative focal length.
(D) one concave surface.
2) The least distance of distinct vision is (A) the near point of the eye.
(C) at infinity.
(B) the far point of the eye.
(D) the focal length of the eye.
3) The radii of curvatures of a convex lens are 0.04 m and 0.04 m. Its refractive index is 1.5, its focal length is (A) 0.04 m
(B) 4 m
(C)
0.4 m
(D)
40 m
4) The minimum value of absolute refractive index is ________. (A) zero
(C) more than one
(B) one
(D) less than zero
5) What is the focal length of a double convex lens for which radius of curvature of the surface is 40 cm (A) 50 cm
? (B) 40 cm
(C) -30 cm
(D) -40 cm
6) Optical instruments, in general, extends our range of vision by (A) making the incident rays subtend a smaller angle at the eye. (B) making the incident rays subtend a larger angle at the eye. (C) producing an inverted image. (D) correcting our vision defects. 7) Hypennetropia can be corrected using _______. (A) concave lens
(C) convex lens
(B) concave mirror
(D) convex mirror
8) The final image produced by a simple microscope is _______. (A) real and erect
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(B) real and inverted
(D) virtual and inverted
9) Image formed by a compound microscope is (A) Real and erect.
(C) Real and inverted.
(B) Virtual and erect.
(D) Virtual and inverted.
10) A compound microscope is focused on a tiny object by (A) changing the separation of the objective and the eyepiece. (B) changing the distance of the object from the objective. (C) changing the focal length of the objective. (D) changing the focal length of the eyepiece. 11)
Magnifying power of a compound microscope is (A)
12)
(B)
(C)
(D)
If the least distance of distinct vision is 25 cm, then convex lens of focal length 5 cm acts as magnifier of magnifying power (A) 5
13)
(B) 10
(C) 12
(D) 6
The length of an astronomical telescope is 40 cm and magnifying power 7. The focal lengths of its lenses will be
14)
(A) +35cm & -5 cm
(C) +35 cm & +5 cm
(B) -35 cm & -5 cm
(D) -35 cm & +5 cm
In normal adjustment, magnification of a astronomical telescope is given by (A)
15)
(B)
(C)
(D)
The radii of curvatures of a convex lens are 24 cm and 8 cm. Its refractive index is 1.5, then its focal length is (A) 8 cm
16)
(B)12 cm
(C) 16 cm
(D) 4 cm
To have larger magnification by a telescope, (A) the objective should be of large focal length and the eyepiece should be of small focal length. (B) the object should be of small focal length and the eyepiece should be of large focal length. (C) both should have large focal length. (D) both should have small focal length.
17)
A convex glass lens
has a focal length of 8 cm when placed in air. What is
the focal length of the lens when it is immersed in water?
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(D) 30 cm
The focal lengths of objective and eye lens of astronomical telescope are 2 m and 5 cm respectively. The magnifying power of telescope if final image is formed at infinity is (A) -100
19)
(B)-60
(C) -80
(D) -40
The focal length of objective of microscope is f0 and that of eyepiece is
. Which of
the following is correct ? (A) 20)
(B)
(C)
(D)
Focal length of the objective of a microscope is (A) greater than the focal length of the eyepiece. (B) less than the focal length of the eyepiece. (C) equal to the focal length of the eyepiece. (D) arbitrary.
21)
22)
The study of light without considering diffraction effect is called as ______. (A) mechanical optics
(C) process of light energy
(B) geometrical straight line process
(D) ray optics
In case of a convex mirror, the image formed is (A) always on opposite side, virtual, erect. (B) always on the same side, virtual, erect. (C) always on opposite side, real, inverted. (D) dependent on object distance.
23)
In front of a concave mirror, an object is placed at the radius of curvature, the image will be formed at _______. (A) at focus (B) at radius of curvature (C) between focus and radius of curvature (D) beyond the radius of curvature
24)
25)
26)
In Cassegrain telescope, objective is ________. (A) convex lens
(C) concave mirror
(B) convex mirror
(D) concave lens
A converging mirror is used in (A) compound microscope.
(C) astronomical microscope.
(B) simple microscope.
(D) cassegrain telescope.
The relation between focal length (f) and radius of curvature (R) of a spherical mirror is
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(B)
(C)
(D)
Magnifying power of astronomical telescope is ‘M.P’. If the focal length of objective is doubled, then the magnifying power for normal adjustment will become (A) 2M.P
28)
29)
(B)
(C)
(D)
An object is placed infront of a convex lens anywhere on its axis. Its image is (A) always real.
(C) sometimes real, sometimes virtual
(B) always virtual.
(D) at distance of distinct vision.
Astronomical telescope has an objective of comparatively (A) large aperture and large focal length. (B) small aperture and small focal length. (C) large aperture and small focal length. (D) small aperture and large focal length.
30)
A convex lens for focal length 4 cm is used as simple microscope. The magnifying power of it, when image is formed at distance of distinct vision is (A) 6.25
31)
(B) 7.25
(C) 8
(D) 8.25
The radii of curvature of a convex lens are 0.05 m and 0.05 m. The refractive index of the material of lens is 1.5, then its focal length is (A) 0.05 m
32)
(B) 0.5 m
For a plano-convex lens,
(C) 5 m
(D) 50 m
the radius of curvature of convex surface is 10 cm
and the focal length is 30 cm. The refractive index of the material of the lens is (A) 1.5 33)
(B) 1.66
(C) 1.33
(D) 2.5
A convex lens made up of glass of R.I. 1.5 has a focal length of 8 cm when placed in air. What is the focal length of the lens when it is immersed in water? (A) 32 cm
34)
35)
(B) 30 cm
(C) 16 cm
(D) 6 cm
In myopia, light from a distant object converges ________. (A) before the retina
(C) after the retina
(B) at the retina
(D) at infinity
A plano-convex lens is made up of refractive index 1.6. The radius of curvature of the curved surface is 60 cm. The focal length of the lens is (A) 50 cm
36)
(B)100 cm
(C) 200 cm
(D) 150 cm
An object is placed infront of a concave mirror at 8 cm from it. The focal length of it is 16 cm. The image distance is (A) -16 cm
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(B)-8 cm
(C) +10.33 cm
(D) +16 cm
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An object is placed infront of a convex mirror at 10 cm from it. The focal length of convex mirror is 15 cm. The image distance is (A) 5 cm
38)
(B) 6 cm
(C) 10 cm
(D) 12.5 cm
The principle of reversibility of light is on the basis of concept of_______. (A) total internal reflection of light (B) refraction of light (C) principal focus (D) conjugate foci
39)
Magnifying power of simple microscope is four, when the image is formed at infinity. The focal length of simple microscope is (A) 8.33 cm
40)
41)
(B) 6.25 cm
(C) 5 cm
(D) 4 cm
Electronic technicians use ________. (A) concave mirror
(C) concave lens
(B) convex mirror
(D) convex lens
A telescope has an objective of focal length 100 cm and an eye-piece of focal length 5 cm. Find the magnifying power of telescope. (A) 20
(B) 95
(C) 105
(D) 500
â?– Answers to Multiple Choice Questions 1. (B)
2. (D)
3. (A)
4. (B)
5. (B)
6. (B)
7. (C)
8. (C)
9. (D)
10. (B)
11. (C)
12. (C)
13. (C)
14. (C)
15. (B)
16. (A)
17. (A)
18. (D)
19. (C)
20. (B)
21. (D)
22. (A)
23. (B)
24. (C)
25. (D)
26. (B)
27. (A)
28. (C)
29. (A)
30. (B)
31. (A)
32. (C)
33. (A)
34. (A)
35. (B)
36. (D)
37. (B)
38. (D)
39. (B)
40. (D)
41. (A)
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