Ray Optics and Optical Instruments · Question 23

Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is F1. When the space between the two lenses is filled with glycerin (which has the same refractive index ( = 1.5) as that of glass) then the equivalent focal length is F2. The ratio F1 : F2 will be :

1. 1 : 2
2. 2 : 3
3. 3 : 4
4. 2 : 1

The refractive index of the material of a prism is 2 and the angle of the prism is 30 . One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is

1. 60
2. 45
3. 30
4. zero

An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be

1. 30 cm away from the mirror
2. 36 cm away from the mirror
3. 30 cm towards the mirror
4. 36 cm towards the mirror

An astronomical refracting telescope will have large angular magnification and high angular resolution, when it has an objective lens of

1. small focal length and large diameter
2. large focal length and small diameter
3. large focal length and large diameter
4. small focal length and small diameter

A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle , the spot of the light is found to move through a distance y on the scale. The angle is given by

1. yx
2. x2y
3. xy
4. y2x

A thin prism having refracting angle 10 is made of glass of refractive index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be

1. 6
2. 8
3. 10
4. 4

Match the corresponding entries of column 1 with column 2. [Where m is the magnification produced by the mirror]

1. (a)-(p) and (s); (b)-(q) and (r); (c)-(q) and (s); (d)-(q) and (r)
2. (a)-(r) and (s); (b)-(q) and (s); (c)-(q) and (r); (d)-(p) and (s)
3. (a)-(q) and (r); (b)-(q) and (r); (c)-(q) and (s); (d)-(p) and (s)
4. (a)-(p) and (r); (b)-(p) and (s); (c)-(p) and (q); (d)-(r) and (s)

An astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance

1. 50.0 cm
2. 54.0 cm
3. 37.3 cm
4. 46.0 cm

The angle of incidence for a ray of light at a refracting surface of a prism is 45 . The angle of prism is 60 . If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are

1. 45 ; 2
2. 30 ; 1 2
3. 45 ; 1 2
4. 30 ; 2

Two identical glass ( g = 3/2) equiconvex lenses of focal length f each are kept in contact. The space between the two lenses is filled with water ( w = 4/3). The focal length of the combination is

1. f/3
2. f
3. 4f/3
4. 3f/4