Ray Optics and Optical Instruments

A spherical surface of radius of curvature R, separates air from glass (refractive index =1.5). The centre of curvature is in the glass medium. A point object 'O' placed in air on the optic axis of the surface, so that its real image is formed at 'I' inside glass. The line OI intersects the spherical surface at P and PO=PI. The distance PO equals to

1. 5R
2. 2R
3. 1.5R
4. 3R

Given a thin convex lens (refractive index 2), kept in a liquid (refractive index 1, 1< 2) having radii of curvatures |R1| and |R2|. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

1. ( 2+ 1)|R1|( 2- 1)
2. 1|R1| |R2| 2 (2|R1|+|R2| )- 1 |R1| |R2|
3. 1|R1| |R2| 2 (|R1|+|R2| )- 1|R1|
4. 1|R1| |R2| 2 (|R1|+|R2| )- 1|R2|

A concave mirror of focal length f in air is dipped in a liquid of refractive index . Its focal length in the liquid will be:

1. f
2. f
3. f
4. f( -1)

The refractive index of the material of a glass prism is 3. The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?

1. 60
2. 50
3. 58
4. 48

In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to |R1| and |R2|, i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is [figure]

1. - 16 ( 1|R1|- 1|R2| )
2. - 16 ( 1|R1|+ 1|R2| )
3. 16 ( 1|R1|+ 1|R2| )
4. 16 ( 1|R1|- 1|R2| )

Given is a thin convex lens of glass (refractive index ) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself?

1. R/
2. R/(2 -1)
3. R/(2 -3)

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature R=2 m. Another car approaches him from behind with a uniform speed of 90 km/hr. When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is ' a '. The value of 100a is m/s2.

A symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in figure. If the power of original lens is 4D then the power of a part of the divided lens is [figure]

1. 2D
2. 8D
3. 4D
4. D