Question:
A beam of light both reflects and refracts at the surface between air and glass. The index of refraction of the glass is \(1.4\). If the refracted and the reflected rays are perpendicular to each other, then the angle of incidence in the air is
A beam of light both reflects and refracts at the surface between air and glass. The index of refraction of the glass is \(1.4\). If the refracted and the reflected rays are perpendicular to each other, then the angle of incidence in the air is
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When the reflected ray and refracted ray are perpendicular to each other, the angle of incidence is called Brewster’s angle and is given by
\[
\tan i=\mu
\]
Updated On: Jun 24, 2026
- \(\tan^{-1}(1.4)\)
- \(\sin^{-1}\left(\dfrac{1}{1.4}\right)\)
- \(\tan^{-1}\left(\dfrac{1}{1.4}\right)\)
- \(\sin^{-1}\left(\dfrac{1.4}{\pi}\right)\)
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The Correct Option is A
Solution and Explanation
Step 1: Use the condition for perpendicular reflected and refracted rays.
When the reflected ray and refracted ray are perpendicular to each other, the angle of incidence is equal to Brewster’s angle.
Therefore, \[ i+r=90^\circ \] where \[ i=\text{angle of incidence} \] and \[ r=\text{angle of refraction} \]
Step 2: Apply Brewster’s law.
According to Brewster’s law, \[ \tan i=\mu \] where \(\mu\) is the refractive index of the second medium with respect to the first medium.
Given, \[ \mu=1.4 \] Thus, \[ \tan i=1.4 \]
Step 3: Calculate the angle of incidence.
Taking inverse tangent on both sides, \[ i=\tan^{-1}(1.4) \]
Step 4: Final conclusion.
Hence, the required angle of incidence is \[ \boxed{\tan^{-1}(1.4)} \]
When the reflected ray and refracted ray are perpendicular to each other, the angle of incidence is equal to Brewster’s angle.
Therefore, \[ i+r=90^\circ \] where \[ i=\text{angle of incidence} \] and \[ r=\text{angle of refraction} \]
Step 2: Apply Brewster’s law.
According to Brewster’s law, \[ \tan i=\mu \] where \(\mu\) is the refractive index of the second medium with respect to the first medium.
Given, \[ \mu=1.4 \] Thus, \[ \tan i=1.4 \]
Step 3: Calculate the angle of incidence.
Taking inverse tangent on both sides, \[ i=\tan^{-1}(1.4) \]
Step 4: Final conclusion.
Hence, the required angle of incidence is \[ \boxed{\tan^{-1}(1.4)} \]
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