Question

Figure 35-28 shows four situations in which light reflects perpendicularly from a thin film of thickness L sandwiched between much thicker materials. The indexes of refraction are given. In which situations does Eq. 35-36 correspond to the reflections yielding maxima (that is, a bright film).

Short answer

The situation corresponding to the reflections yielding maxima is (c).

Step-by-step solution

Given information:

The thickness of the thin film for each situation is L.

The index of refraction of the thin film for situation (a) is 1.6.

The index of refraction of the thin film for situation (b) is 1.6.

The index of refraction of the thin film for situation (c) is 1.3.

The index of refraction of the thin film for situation (d) is 1.6.

Path length difference: 

If two different waves exactly in phase meet each other then they produce fully constructive interference having a bright film.

The formula for the path length difference (2L) of the light in the medium is given by,

$2L=\left(m+\frac{1}{2}\right)\frac{\lambda }{n_2}$

Here, $\lambda$ is the wavelength of the incident light, n₂ is the index of refraction of the medium, and m=0,1,2...... for maxima-bright film in air.

Situation yielding maxima: 

According to the equation 35-36,

$2L=\left(m+\frac{1}{2}\right)\frac{\lambda }{n_2}$

For a particular order, the maximum intensity will be possible when,

$2L\propto \frac{1}{n_2}$

From the above relation, the reflections yield maxima for a medium having the least value of the index of refraction.

Comparing the given four situations,

$1.3<1.6$

So, the value of the index of refraction is the least for situation (c).

Hence, the situation corresponding to the reflections yielding maxima (that is, a bright film) is (c).

Hence, the situation corresponding to the reflections yielding maxima (that is, a bright film) is (c).