# The diameter of a plano-convex lens is 6 cm and thickness at the centre is 3 mm. If the speed of light in the material of the lens is $2×{10}^{8}m}{sec}$, the focal length of the lens is1. 15 cm                          2. 20 cm 3. 30 cm                          4. 10 cm

Subtopic:  Lenses |
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A luminous object is placed at a distance of $$30$$ cm from the convex lens with a focal length of $$20$$ cm. On the other side of the lens, at what distance from the lens, a convex mirror with a radius of curvature of $$10$$ cm be placed in order to have an upright image of the object coincident with it?
 1 $$12~\text{cm}$$ 2 $$30~\text{cm}$$ 3 $$50~\text{cm}$$ 4 $$60~\text{cm}$$
Subtopic:  Lenses |
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Shown in the figure here is a convergent lens placed inside a cell filled with a liquid. The lens has focal length + 20 cm when in air and its material has refractive index 1.50. If the liquid has refractive index 1.60, the focal length of the system is

1. + 80 cm

2. – 80 cm

3. – 24 cm

4. –160 cm

Subtopic:  Lens Makers' Formula |
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Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams

Subtopic:  Lenses |
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The size of the image of an object, which is at infinity, as formed by a convex lens of

focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the

convex lens and the image is at a distance of 26 cm from the convex lens, calculate the

new size of the image.

1. 1.25 cm

2. 2.5 cm

3. 1.05 cm

4. 2 cm

Subtopic:  Lenses |
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An achromatic prism is made by crown glass prism $\left({A}_{c}=19°\right)$ and flint glass prism

$\left({A}_{F}=6°\right)$. If ${}_{C}\mu _{v}=1.5$ and ${}_{F}\mu _{v}=1.66$, then resultant deviation for red coloured ray will

be

1. 1.04°

2. 5°

3. 0.96°

4. 13.5°

Subtopic:  Prisms |
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An isosceles prism of angle 120° has a refractive index of 1.44. Two parallel

monochromatic rays enter the prism parallel to each other in air as shown. The rays

emerging from the opposite faces :

1. Are parallel to each other

2. Are diverging

3. Make an angle $2{\mathrm{sin}}^{-1}\left(0.72\right)$ with each other

4. Make an angle $2\left\{{\mathrm{sin}}^{-1}\left(0.72\right)-30°\right\}$ with each other

Subtopic:  Prisms |
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A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel

to the base inside the prism. If $\mu$ is the refractive index of the material of the prism, the

maximum value of the base angle for which light is totally reflected from the hypotenuse

is

1. ${\mathrm{sin}}^{-1}\left(\frac{1}{\mu }\right)$

2. ${\mathrm{tan}}^{-1}\left(\frac{1}{\mu }\right)$

3. ${\mathrm{sin}}^{-1}\left(\frac{\mu -1}{\mu }\right)$

4. ${\mathrm{cos}}^{-1}\left(\frac{1}{\mu }\right)$

Subtopic:  Total Internal Reflection |
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A plano-convex lens when silvered in the plane side behaves like a concave mirror of

focal length 30 cm. However, when silvered on the convex side it behaves like a concave

mirror of focal length 10 cm. Then the refractive index of its material will be

1. 3.0

2. 2.0

3. 2.5

4. 1.5

Subtopic:  Lenses |
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A ray of light travels from an optically denser to rarer medium. The critical angle for the

two media is C. The maximum possible deviation of the ray will be

1. $\left(\frac{\mathrm{\pi }}{2}-C\right)$

2. 2C

3. $\mathrm{\pi }-2\mathrm{C}$

4. $\mathrm{\pi }-\mathrm{C}$

Subtopic:  Total Internal Reflection |
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