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

the points are closer to each other

Step-by-step 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 =
`(c)/(f) \ (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 =
`(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