Question

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness $h$ in terms of the angle of incidence $i$ and angle of refraction $r$, if the glass slab is placed in air medium?

• A. $\frac{h \, \tan(i - r)}{\tan r}$
• B. $\frac{h \, \cos(i - r)}{\sin r}$
• C. $h$
• D. $\frac{h \, \sin(i - r)}{\cos r}$

Hint:

The lateral shift is affected by the thickness of the glass slab and the angles at which the light enters and exits the slab. Understanding the geometry of refraction in a parallel-sided slab is essential for deriving the shift formula.

Answer 1

The Correct Option is D

The lateral shift of a ray refracted through a parallel-sided glass slab is given by the formula:
$$\Delta x = \frac{h \, \sin(i - r)}{\cos r}$$ This formula can be derived from the geometry of refraction. The ray undergoes refraction at both the entry and exit surfaces of the glass slab, and the lateral shift corresponds to the displacement of the ray after passing through the slab. 
Since the ray travels a distance $h$ in the slab, the shift depends on the angles of incidence $i$ and refraction $r$. 
Thus, the correct option is option (4).