Answer to Question #91180 in Optics for Mary Alao

Question

A ray of light passes from air though a rectangular glass block whose longest parallel sides are 4.5cm apart. Given that the angle of incidence is 52°, determine the lateral displacement of the ray. (Refractive index of glass= 1.5)

Answer 1

Use this formula

$$x=\frac{d sin(\alpha-\beta)}{cos(\beta)}$$

where

$$d=4.5\cdot 10^-2 (m); \alpha=52^o.$$

and

$$\beta=arcsin(\frac{sin(\alpha)}{n})$$ $$\beta=arcsin(\frac{sin(52)}{1.5})=31.7^o$$

lateral displacement of the ray.

$$x=\frac{0.045\cdot sin(52-31.7)}{cos(31.7)}=0.018 (m) = 1.8 (cm)$$