Optical Instruments: Practice Problem & Solution
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: (2017-Delhi)
Solution Explained:
To solve this problem, we apply the core principles of Optical Instruments. Understanding the underlying formula is key to arriving at the correct answer below:
When a plane mirror is rotated by an angle $\theta$, the reflected ray rotates by an angle $2\theta$. For a screen at distance $x$, the displacement of the spot is $y = x \tan(2\theta)$. For small angles, $\tan(2\theta) \approx 2\theta$, so $y = x(2\theta)$, which yields $\theta = \frac{y}{2x}$.
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