Ray Optics and Optical Instruments

A thin biconvex lens is prepared from the glass ( =1.5) both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of cm.

1. 10
2. 12.5
3. 13
4. 13.5

Light ray incident along a vector AO ( AO=2 i-3 j ) emerges out along vector OB ( OB=C i-4 j ) as shown in the figure below. The value of C is . [figure]

1. 1.6
2. 0.16
3. 11.6
4. 16

A spherical interface lens of radius R separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of 4R in front of spherical interface. The magnitude of the magnification of point source image is . [figure]

1. 1.66
2. 2.33
3. 2.66
4. 1.33

Angle of minimum deviation is equal to the half of the angle of prism in an equilateral prism. The refractive index of the prism is .

1. 1.5
2. 3
3. 2
4. 1.65

A concave mirror of focal length 10 cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is cm.

A ray of light passing through an equilateral prism is having velocity 2.12 108 m/s in the prism material, then the minimum angle of deviation is degrees.

1. 45
2. 30
3. 28
4. 58

A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be

1. increased two times
2. increased 32 times
3. decreased two times
4. decreased 32 times

A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses ?

1. behaves as concave lens if |fconvex|>|fconcave|
2. behaves as concave lens if |fconvex|<|fconcave|
3. behaves as convex lens if |fconvex|>|fconcave|
4. Focal length of the lens system will change if the positions of two lenses are interchanged

An object AB is placed 15 cm on the left of a convex lens P of focal length 10 cm. Another convex lens Q is now placed 15 cm right of lens P. If the focal length of lens Q is 15 cm, the final image is .

1. virtual, formed at 7.5 cm right of lens Q, with a size bigger than that of AB
2. real, formed at 7.5 cm right of lens Q, with a size same as that of AB
3. formed at infinity.
4. real, formed at 7 cm right of lens Q, with a size smaller than that of AB

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm as shown in figure. The length of the image is cm. [figure]

1. 2.5
2. 5
3. 7.5
4. 7