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A light ray is incident on a glass plate at an angle of 40 degrees

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A light ray is incident on a glass plate at an angle of 40° as shown in the figure.
a) Find angles Α, Β, and Γ?
b) Will any of the light striking the side of the glass plate at point B pass out through the side?
 
Optics - A light ray is incident on a glass plate (Related to Critical Angle, Snell's Law) Optics - A light ray is incident on a glass plate (Related to Critical Angle, Snell's Law) - Physics Problems
A light ray is incident on a glass plate at an angle of 40° as shown in the figure.
a) Find angles Α, Β, and Γ?
b) Will any of the light striking the side of the glass plate at point B pass out through the side?
 

A light ray is incident on a glass plate

We can find refracted angle at point A by Applying Snell’s Law
Snell's Law
Snell's Law
refracted angle
refracted angle
Using geometry

Θ = 25.37°

Using geometry we can see
(Normal drawn at point A and left side of the glass surface is parallel to each other. There is a special rule used in geometry (the Transversal Postulate) that involves angles and transversals. It says that if two parallel lines are intersected by a transversal, then the corresponding angles are congruent.)

Θ = Α

At point B we have refection, therefore incident angle and reflected angles are the same.

Using geometry we can also get the relation

Α = Β

Α = 25.37°

Β = 25.37°

Snell's Law

We can find angle Γ at point C by Applying Snell’s Law
Gamma
Gamma
Gamma
Critical Angle diagram

Γ = 40°

b) Will any of the light striking the side of the glass plate at point B pass out through the side?

To answerer this part, we need to find the critical angle at point B which internal reflection begins.

Let’s find critical angle for Glass to Air at point B
Snell's Law

Using Snell’s Law
Critical Angle
Critical Angle
Critical Angle


Critical angle is 41.8°

In order for total reflection at point B, incident angle > critical angle

Incident angle = 90° - 25.37°
Incident angle = 64.63°

Critical angle Θc = 41.8°

In this example incident angle > critical angle, therefore we have total reflection at point B. Light ray striking at point B will not pass through the side.
 
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