# What is the minimum thickness of a thin film for maximum light reflection?

• Liquefaction
In summary, the conversation discusses a scenario involving a glass plate coated with a thin film and a beam of monochromatic light incident on its surface. The frequency and wavelength of the light are calculated, as well as the minimum thickness of the film for both the minimum and maximum resultant intensity of the reflected light.
Liquefaction
1984 PHYSICS B WAVES

The surface of a glass plate (index of refraction n3 = 1.50) is coated with a transparent thin film (index of refraction n2 = 1.25). A beam of monochromatic light of wavelength 6.0 X 10-7 meter traveling in air (index of refraction n1 = 1.00) is incident normally on surface S1 as shown above. The beam is partially transmitted and partially reflected.

a) Calculate the frequency of the light.

b) Calculate the wavelength of the light in the thin film.

The beam of light in the film is then partially reflected and partially transmitted at surface S2·

c) Calculate the minimum thickness d1 of the film such that the resultant intensity of the light reflected back into the air is a minimum.

d) Calculate the minimum nonzero thickness d2 of the film such that the resultant intensity of the light reflected back into the air Is a maximum.

You're going to have to show some of your own work first.

a) The frequency of the light can be calculated using the formula f = c/λ, where c is the speed of light (3.0 X 10^8 m/s) and λ is the wavelength of the light (6.0 X 10^-7 m). This gives us a frequency of approximately 5.0 X 10^14 Hz.

b) The wavelength of the light in the thin film can be calculated using the formula λ2 = λ1/n2, where λ1 is the wavelength of the light in air and n2 is the index of refraction of the thin film. Plugging in the values, we get a wavelength of approximately 4.8 X 10^-7 m.

c) To calculate the minimum thickness d1, we can use the formula d1 = λ2/4n2, where λ2 is the wavelength of the light in the thin film and n2 is the index of refraction of the thin film. This gives us a minimum thickness of approximately 1.9 X 10^-7 m.

d) To calculate the minimum nonzero thickness d2, we can use the formula d2 = λ2/2(n2-1), where λ2 is the wavelength of the light in the thin film and n2 is the index of refraction of the thin film. This gives us a minimum nonzero thickness of approximately 3.8 X 10^-7 m.

## What are light waves?

Light waves are electromagnetic waves that are visible to the human eye. They are a form of energy that travels in a straight line and can travel through a vacuum or a medium, such as air or water.

## How do light waves interact with matter?

Light waves can interact with matter in three main ways: reflection, refraction, and absorption. Reflection occurs when light bounces off a surface, while refraction is the bending of light as it passes through a medium with a different density. Absorption, on the other hand, occurs when light is absorbed by matter and converted into other forms of energy.

## What is the difference between a convex and concave lens?

A convex lens is thicker in the middle and thinner at the edges, causing light rays to converge and form a real image. On the other hand, a concave lens is thinner in the middle and thicker at the edges, causing light rays to diverge and form a virtual image.

## How does the human eye see color?

The human eye contains specialized cells called cones that are sensitive to different wavelengths of light. These cones send signals to the brain, which then interprets the different wavelengths as different colors. The combination of these signals allows us to see a wide range of colors.

## What are some practical applications of optics?

Optics has many practical applications, including lenses and mirrors used in cameras, telescopes, and microscopes. It also plays a crucial role in the design of eyeglasses, contact lenses, and laser technology. Optics is also used in communication systems, such as fiber optics, which transmit information through light pulses.

• Introductory Physics Homework Help
Replies
35
Views
1K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
12
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
894
• Introductory Physics Homework Help
Replies
7
Views
5K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
6
Views
3K
• Introductory Physics Homework Help
Replies
1
Views
173
• Introductory Physics Homework Help
Replies
1
Views
680