Question

Consider the diffraction pattern due to a single slit. The first maximum for a certain monochromatic light coincides with the first minimum for red light of wavelength 660 nm. The wavelength of the monochromatic light is:

(a) 485 nm
(b) 495 nm
(c) 505 nm
(d) 515 nm

Answer 1

The wavelength of the monochromatic light is approximately 495 nm.

Step-by-step explanation:

The diffraction pattern due to a single slit produces a central maximum and many smaller and dimmer maxima on either side.

The first maximum for a certain monochromatic light coincides with the first minimum for red light of wavelength 660 nm. To find the wavelength of the monochromatic light, we can use the relationship between the size of the slit and the angle of the first minimum:

sin(θ) = λ / (2 * a)

where θ is the angle of the first minimum, λ is the wavelength, and a is the width of the slit. Since the first maximum coincides with the first minimum for red light of wavelength 660 nm, we can substitute these values into the equation:

sin(θ) = 660 nm / (2 * a)

Solving for the unknown, the wavelength of the monochromatic light is approximately 495 nm (option b).