# Need help with angle of incidence of light through a prism

• batcave1985
In summary, the conversation discusses the direction of a ray of light entering an equilateral 60° glass prism, the refracted index of the prism material for violet light, and questions about the angle of incidence, total internal reflection, and a ray diagram. The calculation for the critical angle is correct, but the expression could be clearer. The ray diagram shown is incorrect as it does not take into account the reflection and refraction of the ray inside the prism.
batcave1985

## Homework Statement

The direction of the ray of light enters equilateral 60° glass prism normal to the surface as shown in attached image
refracted index of the prism material for the violet light is 1.651

(a) What is the angle of incidence on the surface A-B?
(b) Does total internal reflection occur?
(c) Draw a ray diagram to show how light passes through
the prism

## Homework Equations

critical angle-----sin i c= 1/n

## The Attempt at a Solution

My attempt
a) critical angle
sin= 1/1.651
= 37.3°
Not sure if its 90° for the incidence for side A-B

b) Total internal reflections occur because the angle of incidence is greater
then the critical angle

c) i also attached my attempt to the image.

thank you any help would be great

#### Attachments

• prism attempt.jpg
16.2 KB · Views: 395
The calculation seems correct, but the way you expressed it is confusing.
You wrote
"sin= 1/1.651
= 37.3°"

You should have written
"sin θc= 1/1.651
θc = 37.3°"

1 person
dauto said:
The calculation seems correct, but the way you expressed it is confusing.
You wrote
"sin= 1/1.651
= 37.3°"

You should have written
"sin θc= 1/1.651
θc = 37.3°"

thank you any chance you can tell me if my ray diagram in the picture attached is correct?

batcave1985 said:
thank you any chance you can tell me if my ray diagram in the picture attached is correct?

No.

Note that the angle of incidence is defined as the angle the ray encloses with the normal of the surface.
At totalreflecton, the ray is reflected from the surface AB inside the prism, and is incident onto an other side, and then leaves the prism.

ehild

a) The angle of incidence on the surface A-B can be calculated using the law of refraction, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two materials. In this case, we have:

sin i / sin r = n2 / n1

Where n1 is the refractive index of air (approximately 1) and n2 is the refractive index of the prism material (1.651 for violet light). Therefore:

sin i / sin 60° = 1.651 / 1

sin i = sin 60° * (1.651 / 1) = 1.651 * 0.866 = 1.431

i = arcsin(1.431) = 55.4°

So the angle of incidence on the surface A-B is approximately 55.4°.

b) Total internal reflection will occur when the angle of incidence is greater than the critical angle, which can be calculated using the equation you provided:

sin i_c = 1/n

For violet light, the critical angle is therefore:

sin i_c = 1/1.651 = 0.606

i_c = arcsin(0.606) = 37.3°

Since the angle of incidence on surface A-B is greater than the critical angle (55.4° > 37.3°), total internal reflection will occur.

c) I have attached a ray diagram below to show how light passes through the prism. The incident ray enters the prism at an angle of 55.4° and is refracted towards the normal. It then undergoes total internal reflection at the surface B-C, with the angle of reflection being equal to the angle of incidence. Finally, the refracted ray exits the prism at an angle of 55.4° and is bent away from the normal.

A
/ \
/ \
i r
\ /
\ /
B
/ \
/ \
r i
\ /
\ /
C

## 1. What is the angle of incidence of light through a prism?

The angle of incidence of light through a prism refers to the angle at which a beam of light enters the prism. This angle is measured between the incident ray (incoming light beam) and the normal line (a line perpendicular to the surface of the prism at the point where the light enters).

## 2. How is the angle of incidence related to the angle of refraction?

The angle of incidence and the angle of refraction are related by Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two media.

## 3. Can the angle of incidence of light through a prism be changed?

Yes, the angle of incidence can be changed by adjusting the position of the light source or the prism. The angle of incidence can also be manipulated by using lenses or mirrors to direct the light beam at different angles.

## 4. How does the angle of incidence affect the path of light through a prism?

The angle of incidence determines the angle at which the light beam enters the prism, which in turn affects the angle at which it is refracted and the path it takes through the prism. If the angle of incidence is changed, the path of the light beam through the prism will also change.

## 5. Why is the angle of incidence important in understanding the behavior of light in a prism?

The angle of incidence is important because it determines the amount of refraction that occurs as the light beam passes through the prism. This, in turn, affects the separation of the different wavelengths of light (dispersion) and the formation of the spectrum of colors that we see when light passes through a prism.

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