A ray of light is incident on a transparent medium at an angle of 60°. The reflected ray of light is found to be completely polarised. Then, the refractive index of the transparent medium is nearly:
1.73
Refractive Index Calculation for Polarised Light
When a ray of light is incident on a transparent medium and the reflected ray of light is found to be completely polarised, this specific angle of incidence is known as Brewster's angle, also denoted as the angle of polarisation (\(i_p\)). This phenomenon is described by Brewster's Law, which provides a direct relationship between the refractive index of the medium and the angle of polarisation.
Understanding Brewster's Law
Brewster's Law states that when light is incident at a particular angle (Brewster's angle, \(i_p\)) on the interface between two transparent media, the reflected light is completely plane-polarised, and the reflected and refracted rays are perpendicular to each other. The relationship is given by the formula:
\[ \mu = \tan(i_p) \]
Where:
- \(\mu\) is the refractive index of the transparent medium.
- \(i_p\) is Brewster's angle or the angle of polarisation (which is the angle of incidence in this specific condition).
Step-by-Step Refractive Index Determination
Given in the question:
- The angle of incidence is \(60^\circ\).
- The reflected ray of light is found to be completely polarised.
Since the reflected ray is completely polarised, the given angle of incidence is Brewster's angle.
Therefore, \(i_p = 60^\circ\).
Now, we can use Brewster's Law to find the refractive index (\(\mu\)) of the transparent medium:
\[ \mu = \tan(i_p) \]
Substitute the value of \(i_p\):
\[ \mu = \tan(60^\circ) \]
We know that the value of \(\tan(60^\circ)\) is \(\sqrt{3}\).
\[ \mu = \sqrt{3} \]
To find the numerical value, we calculate \(\sqrt{3}\):
\[ \mu \approx 1.73205 \]
Comparing this calculated value with the given options, we find that 1.73 is the closest value.
Comparison with Options
| Option | Value | Match with Calculation |
|---|---|---|
| 1 | 1.73 | Matches closely |
| 2 | 1.62 | Does not match |
| 3 | 1.52 | Does not match |
| 4 | 1.33 | Does not match |
Based on the calculation using Brewster's Law, the refractive index of the transparent medium is approximately 1.73.
Important Questions from Polarization by Reflection
What is the absolute refractive index of kerosene?
The refractive index of water \(_a\mu_w=\frac{4}{3}\) and refractive index of glass \(_a\mu_g=\frac{3}{2}\) . A lens placed in air has focal length 10 cm. What will be its focal length if placed inside water?
The refractive index of water and dense flint glass are 1.33 and 1.65, respectively. A ray of light travels from dense flint glass to water. The refractive index of water with respect to dense flint glass is _______ and the light ray bends _______ the normal in water.
The refractive indices of quartz crystal for right handed and left handed circularly polarized light of wavelength 762.9 nm are 1.5391 and 1.5392 respectively. The angle of rotation produced by the crystal plate of thickness 0.5 mm is:
For which of the following media is the absolute refractive index almost equal to one?
