Ray Optics And Optical Instruments

The Fresnel distance ( ) is the distance at which diffraction effects become significant and the assumptions of ray optics (such as the approximation of light as straight lines) break down. It is determined by the wavelength of light ( ) and the size of the aperture ( ) through which the light passes.

The formula for the Fresnel distance is given by:

Where:

• is the size of the aperture,
• is the wavelength of the light.

This formula shows the relationship between the aperture size and the wavelength in determining the point at which diffraction effects become important.

Correct Answer:

Correct Answer: (C)

The power of a lens is defined as the reciprocal of its focal length. The dimensional formula for the power of a lens is the same as that of the inverse of length, which is . Since power involves only the length dimension, the mass and time have exponents of 0.
Hence, the dimensional formula for the power of a lens is .

The correct option is (A) :

When light is reflected from a surface, the reflected ray is completely polarized at the Brewster's angle. The Brewster's angle is given by the relation: where is the refractive index of the material. For ray B to be completely polarized, the angle of incidence must be the Brewster's angle. For ray B, the angle of incidence is . Therefore, We know that . Hence,

So, the correct option is (E) :

The refractive index is related to the speed of light in a medium and the speed of light in vacuum by the relation . The refractive index of air actually increases with increasing density. This is because the speed of light in a denser medium (like denser air) is lower, thus the refractive index increases. Therefore, the statement "The refractive index of air decreases with its density" is incorrect.

The correct option is (D) : The refractive index of air decreases with its density.

The power of a lens is related to its focal length by the formula: where is the power in diopters (D) and is the focal length in meters. Given that the power of the corrective lens is , we can find the focal length using the formula: Substituting :

The correct option is (B) : concave lens of focal length -25 cm

where:
- is the focal length of the lens,
- is the refractive index of the lens material,
- is the refractive index of the surrounding medium,
- and are the radii of curvature of the lens surfaces.

Given:
- ,
- ,
- .

First, we find the curvature term using the focal length in air ( ):

Next, we use the same curvature term with the focal length in the fluid to find the refractive index of the fluid :

Substitute :

Thus, the refractive index of the fluid is approximately .

So The correct answer is Option(E):1.4 nearest matching answer

Given:

• Focal length of lens , (convex)
• Focal length of lens , (convex)
• Distance between and :
• Point source is placed 12 cm to the left of .
• Final image is formed at infinity.

Step 1: Image Formation by

For , using the lens formula:

Here, (object distance is negative by convention), :

Thus, the image distance (to the right of ).

Step 2: Condition for Final Image at Infinity

For the final image to be at infinity, the image formed by must lie at the focal point of . Therefore:

Conclusion:

The required separation between the lenses is 16 cm.

Answer:

Given parameters:

• Energy flux
• Surface area
• Time duration
• Complete absorption condition

Total energy absorbed:

Momentum of light:

Thus, the correct option is (C): .

Given:

• Apex angle of prism,
• Refractive index,

Step 1: Formula for Minimum Deviation ( )

The angle of minimum deviation is given by:

Step 2: Substitute Known Values

Since :

Step 3: Solve for

Conclusion:

The angle of minimum deviation is .

Answer:

Critical velocity is the highest velocity a fluid can attain while still maintaining laminar (streamlined) flow.
Beyond this speed, the flow becomes turbulent. where is the velocity of the fluid. If exceeds a critical value (typically around 2000 for pipe flow), turbulence occurs.

The velocity of light in a medium with relative permittivity and relative permeability is given by: Where:
- is the velocity of light in vacuum,
- is the relative permittivity,
- is the relative permeability. We are given that the relative permittivity and the relative permeability . Substitute these values into the formula: Now, simplifying the expression:
Thus, the velocity of light in this medium is . So the correct answer is (A) .