Question

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

Answer 1

Answer:

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 = $\frac{c}{f} \ \frac{1}{n}$

          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 = $\frac{1}{n}$  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