Question

A transparent thin film, of uniform thickness and refractive index n₁ (= 1.4), is coated on the convex spherical surface (of radius R), at the one end of a long solid glass cylinder, of refractive index, n₂ (= 1.5), as shown in Fig. Rays of light, parallel to the axis of cylinder, going through the film, from air to glass, get focused at a distance (the opposite way) f₁ , from the film; while the rays going from glass to air, get focused out a distance f₂ from the film. We would then have:

(1) |f₁| = 3R ; |f₂| = 2R

(2) |f₁| = 3R ; |f₂| = 3R

(3) |f₁| = 2R ; |f₂| = 2R

(4) |f₁| = 2R ; |f₂| = 3R

Answer 1

(2) |f₁| = 3R ; |f₂| = 3R

Let |R| = c, be the radius of each surface of film, of thickness t. The focal length, f, of the thin film, according to lens maker’s formula, is

The spherical film, therefore, behaves like a parallel slab; hence there is no deviation in a ray due to its passage through the film. Fig. (a) shows parallel rays, going from air, getting focused at F₁ , inside the glass. For refraction, from film to glass, we have

Using the refraction formula, at a spherical surface;

Fig.(b)shows the parallel rays, going from glass to air. Now

Using the refraction formula: