Question
A beam of light from a source $$L$$ is incident normally on a plane mirror fixed at a certain distance $$x$$ from the source. The beam is reflected back as a spot on a scale placed just above the source $$L.$$ When the mirror is rotated through a small angle $$\theta ,$$ the spot of the light is found to move through a distance $$y$$ on the scale. The angle $$\theta $$ is given by
A.
$$\frac{y}{{2x}}$$
B.
$$\frac{y}{x}$$
C.
$$\frac{x}{{2y}}$$
D.
$$\frac{x}{y}$$
Answer :
$$\frac{y}{{2x}}$$
Solution :
According to the question
$$L =$$ Light source
When the light beams incident normally on the plane mirror, it is reflected back to the point from which it was coming. When the plane mirror is rotated by an angle $$\theta $$, the reflected ray or beam of light must rotate by angle $$2\theta ,$$ from refraction at plane surface theory.
From the figure $$\tan 2\theta = \frac{{BS}}{{SO}} = \frac{y}{x}$$
If the angle is small $$\tan 2\theta \approx 2\theta $$
So, $$2\theta = \frac{y}{x} \Rightarrow \theta = \frac{y}{{2x}}$$
According to the question
$$L =$$ Light source
When the light beams incident normally on the plane mirror, it is reflected back to the point from which it was coming. When the plane mirror is rotated by an angle $$\theta $$, the reflected ray or beam of light must rotate by angle $$2\theta ,$$ from refraction at plane surface theory.
From the figure $$\tan 2\theta = \frac{{BS}}{{SO}} = \frac{y}{x}$$
If the angle is small $$\tan 2\theta \approx 2\theta $$
So, $$2\theta = \frac{y}{x} \Rightarrow \theta = \frac{y}{{2x}}$$
