A mirror constructed from a piece of glass of thickness 0.50cm and refractice in

Question

A mirror constructed from a piece of glass of thickness 0.50cm and refractice index = 1.6. The bottom surface of the glass is painted with a perfectly-reflective silver coating. A light ray traveling through air enters the mirror at an angle of exactly 30 degrees with respect to normal, as shown in the figure. What is the distance d between the points where the ray enters and exits the mirror?

A mirror constructed from a piece of glass of thickness 0.50cm and refractice index = 1.6. The bottom surface of the glass is painted with a perfectly-reflective silver coating. A light ray traveling through air enters the mirror at an angle of exactly 30 degrees with respect to normal, as shown in the figure. What is the distance d between the points where the ray enters and exits the mirror?

Explanation / Answer

n1 sin(theta1) = n2 sin(theta2)

==> 1 sin(30) = 1.6 sin(theta2)

==> sin(theta2) = 0.3125

==> theta2 = 18.21 degrees

so we can find d:

d = 2 (L tan(theta2)) = 2*0.5*tan(18.21) = 0.33 cm

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