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.	\(60~\text{cm}\)

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

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          

1.		2.
3.		4.

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

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°

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 $2{\sin }^{-1}\left(0.72\right)$ with each other

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

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

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

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

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

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

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. $\mathrm{\pi }-\mathrm{C}$