Wave Optics

Given:

• Young’s double slit experiment setup.
• Five statements (A-E) about fringe properties.

Step 1: Analyze Each Statement

(A) Angular separation remains constant when screen is moved away.

True. The angular separation ( ) depends only on wavelength ( ) and slit separation ( ), not on screen distance ( ).

(B) Fringe separation increases when slit separation decreases.

True. Fringe separation ( ) is inversely proportional to slit separation ( ).

(C) Sharpness decreases when source slit width increases.

True. Increasing source slit width reduces coherence, causing fringes to blur.

(D) Distance between fringes decreases when (slit-screen distance) increases.

False. Fringe separation ( ) is directly proportional to , so increasing increases fringe distance.

(E) Central fringe is white with white light source.

True. All wavelengths constructively interfere at the center, producing a white fringe.

Conclusion:

The statement that is NOT true is (D), as it incorrectly claims fringe distance decreases with increasing .

Answer:

Given:

• Unpolarized light incident on a glass slab
• Reflected ray is completely polarized (Brewster's angle condition)
• Angle of refraction,

Step 1: Apply Brewster's Law

At Brewster's angle ( ), the reflected and refracted rays are perpendicular:

Given , we find:

Step 2: Calculate Refractive Index

Brewster's law relates the refractive index ( ) to :

Conclusion:

The refractive index of the glass is 1.73.

Answer:

Step 1: The standard form of a travelling wave equation is: where is the angular frequency, is the wave number, and the wave velocity is given by: Step 2: From the given equation, we compare terms: Step 3: Using the wave velocity formula: Step 4: Therefore, the correct answer is (E).

Step 1: Lens Maker's Formula The focal length of a convex lens in air is given by the lens maker’s formula: where is the refractive index of the lens material, and are the radii of curvature of the lens surfaces.
Step 2: Modified Lens Maker’s Formula in a Medium When the lens is immersed in a medium of refractive index , the modified formula becomes: Dividing both equations:
Step 3: Substituting Given Values
Given:
- Refractive index of the lens:
- Refractive index of water:
- Focal length in air: cm
Thus, the new focal length of the lens in water is 12 cm.

Step 1: When light is reflected from an optically rarer medium, the frequency of the light remains unchanged, as the frequency of light does not depend on the medium.
Step 2: However, the phase of the light changes by , as the reflection from a rarer medium results in a phase shift of .
Step 3: Thus, both the phase and frequency of the light remain unchanged in the reflected wave.