Question

Find the thickness of film of a camera lens coating that minimizes normal reflection in the wavelength range 400 nm to 700 nm. Assume refractive index of film nfilm=1.38 and nglass=1.50

Answer 1

If a wave of light falls over the interface air-film, a portion of light is reflected and the other is transmitted to the film. This light transmitted strikes over the interface film-glass and again a portion of light is reflected and the other is transmitted.

The light reflected in the interface film-glass strikes in the interface film-air and one portion

of light is trasmitted and the other is reflected.

Therefore, in the air we see a superposition of the waves of light reflected in the system

air-film-glass.

The physics situation is shown in the below figure

Therefore, in the air we have interference of waves of light due to a thin film.

To minimize the normal reflection, the waves of light should interfere destructively.

The condition for the destructive interference is that the phase difference between the

waves of light be or .

A wave of light travellig from a medium of refraction index towards a medium of

refraction index undergoes a phase change upon reflection when and

undergoes no phase change if .

Therefore, the wave of light one undergoes a phase change upon reflection in the interface

air-film and the wave of light two undergoes a phase upon reflection in the interface

film-glass.

Therefore there is no difference of phase for reflection.

However there is a difference in way path traveled for the waves of light one and two.

For interference destructive we require the path difference be , but the path diference

is (the wave two traveled by the film of t width).

Therefore the condition for interference destructive is given by:

.

For we have .

For we have .

To minimize the normal reflection in the wavelenght range from 400 nm to 700 nm

the tickness of film should be from 72.5 nm to 127 nm.