Youngs Double Slit Experiment

Young's Double-Slit Experiment: Bandwidth and Wavelength Ratio

In Young's double-slit experiment, two different light beams of wavelengths and produce interference patterns with band widths and respectively. We are given that the ratio between and is 3:2, and we need to find the ratio between and .

Step 1: Bandwidth Formula

The bandwidth (fringe width) in Young's double-slit experiment is given by:

Where:

• is the bandwidth (fringe width).
• is the wavelength of the light.
• is the distance from the slits to the screen.
• is the separation between the slits.

Step 2: Ratio of Bandwidths

We are given that . We can write this as:

Step 3: Simplify the Ratio

The terms and are the same for both wavelengths (since it's the same experimental setup), so they cancel out:

Step 4: Find the Ratio of Wavelengths

Since , we have:

Conclusion

The ratio between and is 3:2.

The fringe width in Young's double slit experiment is given by: where is the wavelength of light, is the distance between the slits and the screen, and is the distance between the slits. When the experiment is performed in a medium with refractive index , the wavelength of light changes. The wavelength of light in a medium is given by: Thus, the fringe width in the liquid becomes: When the experiment is returned to air (with refractive index ), the fringe width will be multiplied by .Therefore, the fringe width in air will be:

Thus, the correct answer is (D): .

Step 1: The apparent depth when viewed through a transparent medium of refractive index and thickness is given by:
Step 2: This formula arises from the concept of refraction, where light appears to travel a shorter distance in a denser medium due to the bending of rays.
Step 3: Since the question asks for the apparent depth of the ink mark, we directly use the formula.
Step 4: Therefore, the correct answer is (B).

Step 1: The intensity of a wave is proportional to the square of its amplitude:
Step 2: Given that the amplitude ratio is , let and .
Step 3: The intensity ratio is:
Step 4: Therefore, the correct answer is (A).

Step 1: The fringe width (bandwidth) in Young’s double slit experiment is given by: where is the wavelength of light, is the distance between the screen and the slits, and is the separation between the slits.
Step 2: Since and remain unchanged, the bandwidth is directly proportional to the wavelength:
Step 3: To reduce the fringe width from to , we must reduce the wavelength accordingly: Step 4: Therefore, the correct answer is (C).

The fringe width in Young’s double-slit experiment is given by the formula:
where:
- is the wavelength of the light,
- is the distance between the screen and the slits,
- is the distance between the slits.
Since the wavelength of blue light ( ) is smaller than that of green ( ) and red ( ) light, the fringe width follows the order:
Hence, the correct answer is (D).

In a Young's double slit experiment, the fringe width is given by the formula: where: - is the wavelength of the light,
- is the distance between the slits and the screen,
- is the distance between the slits.
In this case, we are told that the distance of the screen ( ) and the slit separation ( ) remain constant.
Therefore, the fringe width is directly proportional to the wavelength .
Thus, the fringe width ratio for wavelengths in the ratio 2:3:4 will also be in the same ratio: So, the corresponding fringe width ratio will be 2:3:4.
Therefore, the correct answer is: