Reflection Of Light By Spherical Mirrors

The correct answer is 600
Fringe width is as follows ,




m
⇒ λ = 600 nm
∴ The wavelength of the light will be 600 nm.

To determine the refractive index of the medium, we will use Snell's law, which relates the angle of incidence and refraction to the refractive indices of the two media. Snell’s law is given by:

Here:

• is the refractive index of air, which we assume to be 1.
• is the angle of incidence, given as 45°.
• is the angle of refraction.
• is the refractive index of the medium, which we need to find.

The light ray is deviated by 15° from its original direction. This means the deviation angle from the normal is:

The angle of refraction is, therefore, 30°. Applying these to Snell's law:

We know:

So the equation becomes:

Solve for :

The value of is approximately 1.414. Therefore, the refractive index of the medium is 1.414.

Conclusion: The correct answer is 1.414.

This matches option 3, which is the correct answer.

So, the correct answer is (C) Both A and R are correct and R is the correct explanation of A.

Solution:
The apparent depth of a medium is given by:

Step 1: Calculate the contribution of oil.
For the oil layer of depth and refractive index :

Step 2: Calculate the contribution of water.
For the water layer of depth and refractive index :

Step 3: Total apparent depth.
The total apparent depth is the sum of the apparent depths of the two layers:

Step 4: Simplify the expression.
Taking a common denominator:

Given:

Step 1: Using the refraction formula

The relation between the refractive indices and distances is given by:

Step 2: Substituting the known values

Step 3: Solving for

Step 4: Finding the total distance

The total distance from the object is:

Final Answer:

To solve the problem of determining the angle of refraction when unpolarized light is incident at an angle of 60° on a transparent medium and the reflected ray is completely polarized, we can use Brewster's Law. Brewster's Law states that the tangent of the polarizing angle (also called Brewster's angle) is equal to the refractive index of the medium, or mathematically:

Here, is the angle of incidence which is 60°, and is the refractive index of the transparent medium.

According to Brewster’s Law, when light is incident at the Brewster angle, the reflected ray is completely polarized perpendicular to the plane of incidence, and the angle of incidence is the polarizing angle.

From the relationship given by Snell's Law:

where is the angle of incidence, and is the angle of refraction.

Since the angle of incidence and in such a case where the reflected light is fully polarized, the angle of refraction and the incident angle add up to 90 degrees:

This implies:

Substituting :

Therefore, the angle of refraction in the medium is 30°.

Hence, the correct answer is 30°.

To determine the angle of minimum deviation ( ) for a prism when the refractive index ( ) is given as , we proceed as follows:

First, let's understand the relation between the refractive index, the angle of the prism ( ), and the angle of minimum deviation ( ). The formula for the refractive index in terms of the angle of deviation is:

Given that the refractive index is , we can set up the equation:

We know that . Therefore, the equation becomes:

Canceling from both sides, we get:

Using the identity , we have:

Equating angles since both are sine functions:

Solving for :

• Multiply through by 2 to eliminate the fraction:
• Add to both sides:

Thus, the angle of minimum deviation ( ) is , confirming that the correct answer is .