Question

Assertion :A parallel beam of light travelling in air can be displaced laterally by a parallel transparent slab by distance more than the thickness of the plate . Reason: The lateral displacement of light travelling in air increases with rise in value of refractive index of slab

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

Using the following diagram:

We can write the following equations by looking at triangles:

$\begin{array}{cc}\frac{x}{L}& =\sin ({\theta }_1-{\theta }_2)\\ & =\sin {\theta }_1\cos {\theta }_2-\cos {\theta }_1\sin {\theta }_2\\ \frac{d}{L}& =\cos {\theta }_2\end{array}$

Assuming that the air has a refractive index of 1, we can further write

$\frac{\sin {\theta }_1}{\sin {\theta }_2}=n$

From basic geometry we know that for angles in the first quadrant,

$\cos \theta =\sqrt{1-{\sin }^2\theta }$ Combining these gives

$\begin{array}{cc}x& =\frac{d}{\cos {\theta }_2}(\sin {\theta }_1\cos {\theta }_2-\cos {\theta }_1\sin {\theta }_2)\\ & =d(\sin {\theta }_1-\frac{\sin {\theta }_1\cos {\theta }_1}{n\cos {\theta }_2})\\ & =d\sin {\theta }_1(1-\frac{\sqrt{1-{\sin }^2{\theta }_1}}{n\sqrt{1-\frac{{\sin }^2{\theta }_1}{n^2}}})\\ & =d\sin {\theta }_1(1-\frac{\sqrt{1-{\sin }^2{\theta }_1}}{\sqrt{n^2-{\sin }^2{\theta }_1}})\end{array}$