Light

Step 1: Formula for focal length of two lenses in contact.
When two lenses of focal lengths and are in contact, the focal length of the combination is given by: For two lenses with equal focal lengths , this becomes: Solving for :
Step 2: Analyze options.
- (A) : Incorrect. This would be the case for two lenses in parallel, not in contact.
- (B) : Incorrect. The focal length of the combination is not twice the focal length of one lens.
- (C) : Correct. The focal length of two lenses in contact is half the focal length of one lens.
- (D) : Incorrect. This is not the correct relationship for two lenses in contact.
Step 3: Conclusion.
The focal length of the combination of two converging lenses in contact is .

Step 1: Formula for focal length and power.
The relationship between power ( ) and focal length ( ) is given by the formula: where is the power of the lens in dioptres and is the focal length in meters. Step 2: Given values.
We are given that the power of the convex lens is 2 dioptres, so: Using the formula, we can find the focal length: Step 3: Conclusion.
Thus, the focal length of the lens is 50 cm.

Step 1: Understanding chromatic aberration.
Chromatic aberration occurs due to the dispersion of light into its constituent colors (spectrum). This happens because different colors (wavelengths) of light refract at different angles when passing through a lens, leading to color fringing. Step 2: Solution to chromatic aberration.
An achromatic combination (made by combining a convex lens and a concave lens of different materials) is designed to minimize chromatic aberration. This combination corrects the color distortion by canceling out the effects of dispersion.
Step 3: Conclusion.
Thus, an achromatic combination is used to reduce chromatic aberration in lenses.

Step 1: Understanding polarization.
Polarized light refers to light in which the vibrations occur in a single plane. The plane of polarization is the direction in which the electric field vector of the light oscillates.
Step 2: Angle between vibration and polarization plane.
In polarized light, the plane of vibration and the plane of polarization are at a right angle, i.e., apart. This means that the light wave’s electric field oscillates in a direction perpendicular to the plane of polarization.
Step 3: Conclusion.
Thus, the angle between the plane of vibration and the plane of polarization is .

Step 1: Photoelectric effect overview.
The photoelectric effect occurs when light strikes a material and ejects electrons from it. The current produced depends on the number of ejected electrons, which is influenced by the intensity of the incident light.
Step 2: Effect of intensity.
When the intensity of the incident light increases, more photons hit the material, leading to the emission of more electrons. This increases the photoelectric current.
Step 3: Elimination.
- (A) increases: Correct, the photoelectric current increases with intensity.
- (B) decreases: Incorrect, as the current increases with intensity.
- (C) remains unchanged: Incorrect, as intensity affects the current.
- (D) first increases then remains constant: Incorrect, current continuously increases with intensity.
Step 4: Conclusion.
Thus, the photoelectric current increases with the intensity of the incident light.

Step 1: de Broglie wavelength.
According to de Broglie’s hypothesis, every moving particle has a wave associated with it. The wavelength of the de Broglie wave is given by: where is Planck's constant and is the momentum of the particle.
Step 2: Dependence of wavelength.
The momentum is related to the mass and velocity of the particle: Thus, the de Broglie wavelength depends on the mass and velocity of the particle, but not on its charge.
Step 3: Elimination.
- (A) mass: The wavelength depends on mass, as momentum depends on mass.
- (B) charge: Correct, charge does not affect the de Broglie wavelength.
- (C) velocity: The wavelength depends on velocity, as momentum is velocity-dependent.
- (D) momentum: The wavelength depends on momentum, as per de Broglie's relation.
Step 4: Conclusion.
Thus, the de Broglie wavelength does not depend on the charge of the particle.

Step 1: Kinetic mass of photon.
The kinetic mass of a photon can be expressed in terms of its energy and speed of light . According to Einstein’s equation for energy and mass relation: For a photon, its energy is also given by , where is Planck’s constant and is the frequency of the photon. Combining these: Solving for :
Step 2: Analyze options.
- (A) : Incorrect. This does not correctly relate the energy and mass of a photon.
- (B) : Correct. This matches the correct formula for the kinetic mass of a photon.
- (C) : Incorrect. This is not the correct formula for the kinetic mass.
- (D) : Incorrect. This does not match the formula.
Step 3: Conclusion.
The correct formula for the kinetic mass of a photon is .

Step 1: Understanding the superposition principle.
When two waves of equal amplitude and wavelength superimpose, the resultant amplitude is determined by the phase difference between the waves.
Step 2: Amplitude and phase difference.
The amplitude of the resultant wave will be maximum when the two waves are in phase, i.e., when the phase difference between them is zero. This results in constructive interference.
Step 3: Conclusion.
Thus, the amplitude will be maximum when the phase difference is zero.