Question

For a given single slit, the diffraction pattern is obtained on a screen first by using red and then by blue light. In which case, will the central maxima, in the observed diffraction pattern have a larger angular width?

Answer 1

Hint: Use the formula for the angular width of the central maxima for the single slit diffraction of the light. This formula gives the relation between the angular width of the central maxima, wavelength of the light and width of the slit. Derive the relation between the angular width of the central maxima and wavelength of the light.

Formula used:
The angular width of the central maxima in the single slit diffraction of light is
\[2\theta = \dfrac{{2\lambda }}{d}\] …… (1)
Here, \[\theta \] is the angular width of the central maximum, \[\lambda \] is the wavelength of the light and \[d\] is the width of the slit.

Complete step by step answer:
We have given that the single slit diffraction pattern is obtained on a screen using red and blue light. From equation (1), it can be concluded that the angular width of the central maxima is directly proportional to the wavelength of the light and inversely proportional to the slit width.

The width of the slit is constant in both the cases when the diffraction pattern is obtained using red as well as blue light.Hence, the angular width is only directly proportional to the wavelength of the light. The wavelength of the red light is greater than the wavelength of the blue light.

Hence, the angular width of the central maxima is greater for the red light as it has longer wavelength than the blue light.

Note:The students should be careful while solving the question as we have asked the angular width of the central maxima for the single slit diffraction pattern and not for Young’s double slit experiment. The students should be careful while comparing the wavelengths of the blue and red light.