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Question

Physics Question on Spherical Mirrors

A spherical surface of radius of curvature R, separates air (refractive index 1.0) from glass (refractive index 1.5). The centre of curvature is in the glass. A point object P placed in air is found to have a real image Q in the glass. The line PQ cuts the surface at a point O and PO = O The distance PO is equal to

A

5 R

B

3 R

C

2 R

D

1.5 R

Answer

5 R

Explanation

Solution

The correct option is(A): 5 R.

Let us say PO = OQ = X
Applyingμ2vμ1u=μ1μ2R\, \, \, \, \, \, \, \, \frac{\mu_2}{v}-\frac{\mu_1}{u}=\frac{\mu_1-\mu_2}{R}
Substituting the values with sign
1.5+X1.0X=1.51.0+R\frac{1.5}{+X}-\frac{1.0}{-X}=\frac{1.5-1.0}{+R}
(Distances are measured from O and are taken as positive in
the direction of ray of light)
\therefore\hspace15mm \frac{2.5}{X}=\frac{0.5}{R}
\therefore\hspace15mm X=5R