Question

A narrow beam of white light enters a prism made of crown glass at a 45 degree incident angle, as shown below. At what angles from perpendicular to the exiting surface, do the red (660 nm) and violet (410 nm) components of the light emerge from the prism? Hint Red light is refracted at 53.5 degrees from the perpendicular; violet light is refracted at 55.63 degrees from the perpendicular, and the difference between the angles of refraction of two colors is 0.356 degrees. 60° Incident light 45° Red (660 nm) 60° 60° Violet (410 nm)

          A narrow beam of white light enters a prism made of crown glass at a 45 degree incident angle, as shown below. At what angles from perpendicular to the exiting surface, do the red (660 nm) and violet (410 nm) components of the light emerge from the prism?
Hint
Red light is refracted at 53.5 degrees from the perpendicular; violet light is refracted at 55.63 degrees from the perpendicular, and the difference between the angles of refraction of two colors is 0.356 degrees.
60°
Incident light
45°
Red (660 nm)
60°
60°
Violet (410 nm)

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$A narrow beam of white light enters a prism made of crown glass at a 45 degree incident angle, as shown below. At what angles from perpendicular to the exiting surface, do the red (660 nm) and violet (410 nm) components of the light emerge from the prism? Hint Red light is refracted at 53.5 degrees from the perpendicular; violet light is refracted at 55.63 degrees from the perpendicular, and the difference between the angles of refraction of two colors is 0.356 degrees. 60° Incident light 45° Red (660 nm) 60° 60° Violet (410 nm)$

Added by Rebecca L.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Kelan H

03/22/2022

Step 1

512 and the incident angle is 27.87 degrees, we can use Snell's Law to find the exit angle for red light: \[ n_1 \times \sin(\theta_1) = n_2 \times \sin(\theta_2) \] \[ 1 \times \sin(27.87) = 1.512 \times \sin(\theta_2) \] \[ \sin(\theta_2) = Show more…

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A narrow beam of white light enters a prism made of crown glass at a 45 degree incident angle, as shown below. At what angles from perpendicular to the exiting surface, do the red (660 nm) and violet (410 nm) components of the light emerge from the prism? Red light is refracted at 53.5 degrees from the perpendicular; violet light is refracted at 55.63 degrees from the perpendicular, and the difference between the angles of refraction of two colors is 0.356 degrees.

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Transcript

00:01 As a white light is passing through the prism, so it will divide it in seven colors as the vibrae.

00:10 But here we are talking about only two colors that is of red and violet.

00:14 Here we can increase from both the sides the ray which is incident and we will make an angle that is of theta a, theta b.

00:26 And it is incident at an angle 45 degree that is our white light from the prism.

00:38 The angle of the prism are all contained 60 degree 60 degree and 60 degree.

00:53 Here this light is of red color so we will write here red.

00:58 We know that for the different medium the different refractive index are for follows.

01:07 So we will write here the different refractive indexes as for air refractive index is 1.

01:18 For red colour and for glass it will be 1 .512 and for violet colour for the glass it will become 1 .530.

01:45 By a applying the snail's law by applying the snail's law for red color.

02:18 We know that sine n1, sine theta 1.

02:25 Theta 1, either angle is 45 degree, which is our incident angle, equal to n2, that is our another major.

02:34 That medium is glass because it is coming from air and it is going in the glass theta a is the another angle and one is the air medium we will write one multiply by the value of sign 45 degree is equal to and to the another medium glass for red color sine theta a sine theta a will be equal to 0 .4667.

03:15 So our overall angle will be theta a, that sine a will be going the inverse formation and our answer will be 27 .87 degree.

03:27 This is our angle theta a.

03:39 Now we have to find it out our angle theta b...

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