Question

Prove that a ray of light incident on the surface of a sheet of plate glass of thickness $t$ emerges from the opposite face parallel to its initial direction but displaced sideways, as in Fig. 35-37. Show that, for small angles of incidence $\theta$, this displacement is given by $$x=t \theta \frac{n-1}{n}$$ where $n$ is the index of refraction of the glass and $\theta$ is measured in radians.

          Prove that a ray of light incident on the surface of a sheet of plate glass of thickness $t$ emerges from the opposite face parallel to its initial direction but displaced sideways, as in Fig. 35-37. Show that, for small angles of incidence $\theta$, this displacement is given by
$$x=t \theta \frac{n-1}{n}$$
where $n$ is the index of refraction of the glass and $\theta$ is measured in radians.

Added by Amber L.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sikandar Baig

05/23/2022

Step 1

Step 1: Start with the formula for the displacement of the ray in the glass, which is given by $X = t \cdot \theta \cdot \frac{n-1}{n}$. Show more…

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Prove that a ray of light incident on the surface of a sheet of plate glass of thickness $t$ emerges from the opposite face parallel to its initial direction but displaced sideways, as in Fig. 35-37. Show that, for small angles of incidence $\theta$, this displacement is given by $$x=t \theta \frac{n-1}{n}$$ where $n$ is the index of refraction of the glass and $\theta$ is measured in radians.