Question

A beam of light strikes a sheet of glass at an angle of 56.6° with the normal in air. You observe that red light makes an angle of 38.4° with the normal in the glass, while violet light makes a 36.4° degree angle.

1.What are the indexes of refraction of this glass for these colors of light?

2.What are the speeds of red and violet light in the glass?

Answer 1

(a). Index of refraction are
`n_(red)` = 1.344 &
`n_(violet)` = 1.406

(b). The velocity of red light in the glass
`v_(red) =` 2.23 ×
`10^(8) \ (m)/(s)`

The velocity of violet light in the glass
`v_(violet) =`2.13 ×
`10^(8) \ (m)/(s)`

Step-by-step explanation:

We know that

Law of reflection is

`n_1 \sin\theta_(1) = n_2 \sin\theta_(2)`

Here

`\theta_1` = angle of incidence

`\theta_2` = angle of refraction

(a). For red light

1 ×
`\sin 56.6` =
`n_(red)` ×
`\sin 38.4`

`n_(red)` = 1.344

For violet light

1 ×
`\sin 56.6` =
`n_(violet)` ×
`\sin 36.4`

`n_(violet)` = 1.406

(b). Index of refraction is given by

`n = (c)/(v)`

`n_(red)` = 1.344

`v_(red) = (c)/(n_(red) )`

`v_(red) = (3(10^(8) ))/(1.344)`

`v_(red) =` 2.23 ×
`10^(8) \ (m)/(s)`

This is the velocity of red light in the glass.

The velocity of violet light in the glass is given by

`v_(violet) = (3(10^(8) ))/(1.406)`

`v_(violet) =`2.13 ×
`10^(8) \ (m)/(s)`

This is the velocity of violet light in the glass.