Question

An object is placed at distance X from a thin prism. If the distance between the object and its image is Y then deviation produced by the prism is

• A. $\delta =\frac{Y}{X}$
• B. $\delta =XY$
• C. $\delta =X^{2}Y$
• D. $\delta =X+Y$

Answer 1

The correct option is A $\delta =\frac{Y}{X}$

$\begin{array}{cc}& \text{For very thin prism}\\ & \tan \theta =\theta \\ & \tan \alpha =\frac{h}{x}=\alpha -\left(i\right)\\ & \tan \beta =\frac{h}{y-x}=\beta -\left(ii\right)\\ & \text{in}△ABC,\\ & \alpha +\beta =\delta -\left(iii\right)\\ & \frac{h}{x}+\frac{h}{y-x}=\delta \\ & \frac{hy}{x(y-x)}=\delta \\ & \delta =\frac{\beta y}{x}\\ & \beta =1\delta =\frac{y}{x}\end{array}$