Question

In the figure given below, APB is a curved surface of radius of curvature 10 cm separating air and a transparent material \((μ = \frac{4}{3} ).\) A point object O is placed in air on the principal axis of the surface 20 cm from P. The distance of the image of O from P will be _____.
Fill in the blank with the correct answer from the options given below

• A. 16 cm left of P in air
• B. 16 cm right of P in water
• C. 20 cm right of P in water
• D. 20 cm left of P in air

Answer 1

The Correct Option is A

Step 1: Understanding the Formula

The formula governing the refraction at a spherical surface is:

1 / v - 1 / u = (μ2 - μ1) / R

Where:

• v is the image distance
• u is the object distance
• μ1 is the refractive index of the medium from which the light is coming (air, μ1 = 1)
• μ2 is the refractive index of the medium into which the light is refracted (μ2 = 4/3 for the transparent material)
• R is the radius of curvature of the spherical surface (given as R = 10 cm)

 

Step 2: Substituting the Known Values

Substitute the known values into the formula:

1 / v - 1 / (-20) = (4 / 3 - 1) / 10

Given:

• μ1 = 1 (for air)
• μ2 = 4 / 3 (for the transparent material)
• u = -20 cm (object distance, negative because the object is in front of the surface)
• R = 10 cm (radius of curvature)

 

Step 3: Simplifying the Equation

Now, substitute these values into the equation:

1 / v + 1 / 20 = (1 / 3) / 10

Simplifying the right-hand side:

1 / v + 1 / 20 = 1 / 30

Step 4: Solving for v

Rearranging the equation to find 1 / v:

1 / v = 1 / 30 - 1 / 20

Finding a common denominator:

1 / v = 2 / 60 - 3 / 60 = -1 / 60

Thus,

v = -16 cm

Step 5: Interpreting the Result

The negative sign indicates that the image is formed to the left of point P in air. The image distance is 16 cm.

Final Answer: The distance of the image of O from P will be 16 cm left of P in air.

The correct option is Option A: 16 cm left of P in air