Question

A convex spherical refracting surface with radius R separates a medium having refractive index 5/2 from air.An object is moved towards the surface from far away from the surface along the central axis,its image-
a) changes from real to virtual when it is at a distance R from the surface.
b) changes from virtual to real when it is at a distance R from the surface.
c) changes from real to virtual when it is at a distance 2R/3 from the surface.
d) changes from virtual to real when it is at a distance 2R/3 from the surface.

Answer 1

Answer on Question #49688, Physics, Optics

A convex spherical refracting surface with radius R separates a medium having refractive index 5/2 from air. An object is moved towards the surface from far away from the surface along the central axis, its image-

a) changes from real to virtual when it is at a distance R from the surface.

b) changes from virtual to real when it is at a distance R from the surface.

c) changes from real to virtual when it is at a distance $2R/3$ from the surface.

d) changes from virtual to real when it is at a distance $2R/3$ from the surface.

Solution:

$OP = -u, PI = v$ and $R = PC$

$OP = -u, PI = -v$ and $R = PC$

$$\frac {\mu_ {1}}{- u} + \frac {\mu_ {2}}{v} = \frac {\mu_ {2} - \mu_ {1}}{R}$$

As the object distance is gradually reduced, the conjugate image point $\mathbf{P}$ gradually changes from real to virtual.

The image will be at $v = \infty$ when

$$\frac {1}{- u} + \frac {\mu_ {2}}{\infty} = \frac {3}{2 R}$$ $$- u = \frac {2 R}{3}$$

Answer: c) changes from real to virtual when it is at a distance 2R/3 from the surface.

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