Light Reflection And Refraction

The refraction at a spherical surface is governed by the equation: where:
(refractive index of the rarer medium),
(refractive index of the denser medium),
(object distance, negative as it is measured opposite to the direction of incident light),
(radius of curvature, positive as the center of curvature lies in the denser medium),
is the image distance to be determined.
Substitute the values into the equation:
Simplify:
Simplify further: Solve for : The negative sign indicates that the image is formed on the opposite side of the refracting surface, i.e., in the denser medium.
Final Answer: The distance of the image from the pole of the surface is:

Step 1: Write the Expression for

The net intensity is given by:

Using the trigonometric identity :

Step 2: Use the Given Value for

Substitute :

Simplify for :

Step 3: Solve for

Assuming simplifies, take the square root:

From trigonometric solutions, and .

Step 4: Solve for

Divide by 2 to find :

Final Answer:

The values of are:

Step 1: Apparent Depth of

The relationship between apparent depth and real depth in a medium is given by:

where:

• ,
• (refractive index of the medium).

Substitute the values:

Step 2: Distance Between and

1. Total real depth of the liquid column:
2. Refracted depth (Apparent shift):
3. Distance between and :

Final Answer:

• Apparent depth of :
• Distance between and :

We are given the refractive index of a liquid and the angle of an equilateral prism. We need to find the angle of minimum deviation.

Solution

1. Formula for Refractive Index at Minimum Deviation:

The refractive index of the prism material is given by:

where:

• is the refractive index
• is the angle of the prism
• is the angle of minimum deviation

2. Substitute Given Values:

Given and , we have:

3. Solve for :

We know , so:

Final Answer

Thus, the angle of minimum deviation is .