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Ray Optics and Optical Instruments

Multiple Choice Questions

351.
Two thin lenses when placed in contact, then the power of combination is +10D. If they are kept 0.25 m apart, then the power reduces to +6D. The focal lengths of the lenses (in m) will be

0.5 and 0.125

0.5 and 0.75

0.125 and 0.75

Both have same focal length i.e. 1.25

0.5 and 0.125

$When lenses are in contact, then power P = \frac{1}{F} = \frac{1}{f_{1}} + \frac{1}{f_{2}} 10 = \frac{1}{f_{1}} + \frac{1}{f_{2}} . . . . . (i) When they are placed at distance d apart P' = \frac{1}{F'} = \frac{1}{f_{1}} + \frac{1}{f_{2}} - \frac{d}{f_{1} f_{2}} 6 = \frac{1}{f_{1}} + \frac{1}{f_{2}} - \frac{0.25}{f_{1} f_{2}} . . . . . (ii) From Eqs . (i) and (ii), we get f_{1} f_{2} = \frac{1}{16} . . . . (iii) From Eqs . (i) and (iii), we get f_{1} + f_{2} = \frac{5}{8} . . . . (iv) Also, {(f_{1} - f_{2})}^{2} = {(f_{1} + f_{2})}^{2} - 4 f_{1} f_{2} = (\frac{5}{8}) - 4 \times \frac{1}{16} = \frac{9}{64} or f_{1} - f_{2} = \frac{3}{8} . . . . . (v) Solving Eqs . (iv) and (v), we get f_{1} = 0.5 m an f_{2} = 0.125 m$

352.

The focal length of the objective and eye lenses of a microscope are 1.6 cm and 2.5 cm respectively. The distance between the two lenses is 21. 7 cm. If the final image is formed at infinity, then the linear magnification is

353.

A thin prism placed in air produces minimum deviation of 4° in a light ray. If the prism 8 m is immersed in water, then the minimum deviation produced by it is

354.

An astronomical telescope arranged for normal adjustment has a magnification of 6. Ifthe length ofthe telescope is 35cm, then the focal length of objective and eye piece respectively, are

30 cm, 5 cm
5 cm, 30 cm
40 cm, 5 cm
30 cm, 6 cm

355.

A plane mirror produces a magnification of

zero
- 1
+ 1
between 0 and + 1

356.

In a pond of water, a flame is held 2 m above the surface of water. A fish is at depth of 4 m from water surface.Refractive index of warer i $\frac{4}{3}$ . The apparent height of the lame from the eyes of fish is

5.5 m
6 m
$\frac{8}{3} m$
$\frac{20}{3} m$

357.

White light is incident on the interface of glass and air, as shown in the figure. If green light is just totally and internally reflected then the emerging ray in air contains

all colours
yellow, orange and red
violet, indigo and blue
all colours except green

358.

A convex lens made up of a material of refractive index µ₁ is immersed in a medium of refractive index µ₂ as shown in the figure. The relation between µ₁ and µ₂ is

µ₁ < µ₂
µ₁ > µ₂
µ₁ = µ₂
$μ_{1} = \sqrt{μ_{2}}$

359.

If a flint lens glass of dispersive power 0.066 renders achromatic to a convex lens of crown glass of focal length 60 cm and dispersive power 0.033, then its focal length is