A light spectrum is formed on the screen using a diffraction grating. The entire apparatus made up of laser, grating and the screen is now immersed in a liquid with refractive index 1.33. Do the bright spots on the screen get closer together, farther apart, remain the same or disappear entirely? Explain

the points are closer to each other

Explanation:

The expression for the diffraction of a grating is

         d sin θ = m λ

         sin θ = m λ / d            (1)

where d is the distance between slits and m is the order of diffraction, the most general is to work in the order m = 1, the angle te is the angle of diffraction

When we immerse the apparatus in a medium with refractive index n = 1.33, the light emitted by the laser must comply

         v = λ f

where v is the speed of light in the medium, the frequency remains constant

velocity and refractive index are related

          n = c / v

          v = c / n

we substitute

          c / n = λf

          λ =

          λ = λ₀ / m

where λ₀ is the wavelength in vacuum

we substitute is equation 1

         d sin θ = m λ₀ / n

         sin θ =  λ₀/ n d

         sin θ =  sin θ₀

we can see that the value of the sine is redueced since the refractive index is greater than 1,

consequently the points are closer to each other