Discussion Forum

1)

 A transparent thin film of uniform thickness and refractive index n₁=1.4 is coated on the convex spherical surface of radius  R at one end of a long solid glass cylinder of refractive index n₂=1.5, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance f₁ from the film, while rays of light traversing from glass to air get focused at distance f₂ from the film, then

 

Answer:

Option A,C

Explanation:

$\frac{1}{f_{film}}=(n_{1}-1)\left(\frac{1}{R}-\frac{1}{R}\right)$

$\Rightarrow$  $f_{film}=\infty $           (infinite)

$\therefore$ There is no effect of presence  of  film.

From Air to Glass

  Using  the equation

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

  $\frac{1.5}{v}-\frac{1}{\infty}=\frac{1.5-1}{R}$

 $\Rightarrow$    v=3R

  $\therefore$ f₁=3R

From Glass to Air, Again using  same equation

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

  $\Rightarrow$   $ \frac{1}{v}-\frac{1.5}{\infty}=\frac{1-1.5}{-R}$

$\Rightarrow$  v=2R

      $\therefore$ f₂= 2R