Question

Diffraction pattern is obtained using red light. What will happen if it is replaced by violet light?

• A. Bands will disappear.
• B. Bands will become narrow
• C. Bands will get spaced apart.
• D. Bands will remain unchanged

Hint:

The diffraction pattern depends on the wavelength used. Red light has a longer wavelength than blue. 

Answer 1

The Correct Option is B

In the diffraction pattern, the width of the fringe is given as \(D \lambda \over d\).

As \(\lambda_v < \lambda_r \: \therefore \) the wavelength decreases when the red light is replaced by blue. Hence, the width of the fringe decreases and the pattern becomes narrower.

Answer 2

Diffraction is the bending of the light around the corners of an obstacle into the geometrical shadow of the obstacle. The diffraction pattern depends on the wavelength used. The position of the maxima-minima is directly proportional to the wavelength of the light that is used.

Formula Used

• The position of the band is given by, \(y_n=\frac{nλD}{d}\) where n is the order of the bands, λ is the wavelength of the light, D is the distance from the screen to the slit and d is its width.
• The angular width of the bands is given by the relation \(dsin⁡θ_n=nλ\) where d is the width of the slit, θ is the angular width of the bands, n is the order of the bands and λ is the wavelength of the light used.

Reason

As we can see through the formula that the Angular width is directly proportional to the wavelength. Red light has the maximum wavelength while Violet light has the minimum wavelength.

Hence, as the wavelength decreases, the bands will be narrower.

Thus, the correct option is B) Bands will become narrow

Note: Here, the formula for the position of the bands is used assuming that the angular width θ of the bands is small. If θ is small, \(sinθ≈θ\) and equation (3) can also be expressed as \(dθ_n=nλ\). Maxima is a fringe of high intensity and minima is a fringe of zero intensity.