Problem 74 - Master Resource Book in JEE Main Physics

Question

Assertion Thin films such as soap bubble or a thin layer of oil on water show beautiful colours when illuminated by white light. Reason It happens due to the interference of light reflected from the upper surface of the thin film.

Step-by-Step Solution

Answer

The assertion is true; it occurs due to interference of reflected light from the film's surfaces.

Step 1: Understanding the Assertion

The assertion states that thin films, like soap bubbles or thin oil layers, display a range of colors when white light shines on them. This is an observational fact that suggests an interaction between the film and light that results in colorful patterns.

Step 2: Grasping the Reason

The reason given is that these colors are due to the interference of light waves. When light hits the film, some waves reflect off the top surface, while others penetrate and reflect off the bottom surface. The two sets of waves then interact.

Step 3: Explaining Light Interference

Light waves can constructively or destructively interfere depending on their path difference. Constructive interference amplifies specific colors (wavelengths), whereas destructive interference cancels others, resulting in the observed colors. The interference depends on film thickness, light angle, and wavelength.

Step 4: Connecting Reason to Assertion

The reason accurately explains the assertion. The colorful appearance of thin films is indeed due to interference, which modifies the intensity of specific wavelengths of reflected light, leading to the observation of vibrant colors.

Key Concepts

Constructive Interference

When light hits the surface of a thin film, like a soap bubble, some of the light waves are reflected off the top layer. At the same time, other light waves penetrate the film, reflect off the bottom surface, and travel back up. These two sets of waves can interact with each other in different ways. When the waves align in such a manner that their peaks coincide, we observe constructive interference.

This type of interference occurs when the optical path difference between the two waves is an integer multiple of the wavelength. In simple terms, if the extra distance traveled by the wave inside the film—compared to the wave that only reflects off the top surface—is a whole number of wavelengths, the waves reinforce each other. This results in amplified brightness or vivid colors.

• The condition for constructive interference is given by: \( m \cdot \lambda = 2nd \cdot \cos \theta\), where \( m\) is an integer (0, 1, 2,…), \( \lambda\) is the wavelength of light, \( n\) is the refractive index, and \( d\) is the thickness of the film.

This phenomenon is what causes specific colors to stand out when you look at thin films under light.

Destructive Interference

Destructive interference is the opposite of constructive interference. Here, the peaks of one wave coincide with the troughs of another, leading to their cancellation. This occurs when the optical path difference is a half-integer multiple of the wavelength, like \( (m + 0.5)\lambda\).

When light reflects off the top and bottom surfaces of a thin film, and the optical path difference is such that \( 2nd \cos \theta = (m + 0.5) \lambda \), the waves cancel each other out. As a result, certain wavelengths are reduced or completely eliminated. This means those specific colors won’t appear in the reflected light.

• Destructive interference is key in determining which colors are subtracted from the visible light spectrum.
• The vibrancy of observed colors depends significantly on which wavelengths are undergoing destructive interference.

The absence of particular wavelengths due to destructive interference is why thin films exhibit a spectrum of colors that seem to shift and change.

Optical Path Difference

Optical path difference (OPD) is a critical concept that helps to explain how thin film interference works. It refers to the difference in the paths taken by two light waves inside the film.

The OPD is influenced by several factors:

- The thickness of the film (\( d\)).
- The angle of incident light (\( \theta\)).
- The refractive index of the film (\( n\)).

When light strikes the film, some reflects directly off the surface while other parts transmit, reflecting off the back surface of the film, creating a difference in the optical paths traveled.

This path difference determines whether the interference is constructive or destructive. Essentially, OPD translates into phase differences between waves, leading to interference patterns. Therefore, by controlling these factors, we can manipulate the resulting interference and the colors observed.

The formula for optical path difference is: \(OPD = 2nd \cos \theta\). Understanding OPD allows for predicting and explaining the interplay of light with thin films, resulting in the mesmerizing colors we observe.