A convex spherical refracting surface with radius R separates a medium having refractive index 5/2 from air. As an object is moved towards the surface from far away from the surface along the principle axis. Which of the following are incorrect

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its image changes from real to virtual when it is at a distance R from the surface

its image changes from virtual to real when it is at a distance R from the surface

its image changes from real to virtual when it is at a distance 2R/3 from the surface

its image changes from virtual to real when it is at a distance 2R/3 from the surface

answer is A, B, D.

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Detailed Solution

$\frac{2.5}{v} - \frac{1}{- u} = \frac{2.5 - 1}{R}$

$\frac{2 .5}{v} = \frac{1 .5}{R} - \frac{1}{u}$

$v = \frac{2 .5 uR}{1 .5 u - R};$

$for, v = \infty, 1 .5 u - R = 0 \Rightarrow u = \frac{2 R}{3}$

$For u < \frac{2 R}{3}, v < 0, virtual image$

$u > \frac{2 R}{3}, v > 0, real image$

So, image is changing form real to virtual at $u = \frac{2 R}{3}$

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