Numerical Problems:

Speed of Light:

Solution:

Given: Speed of light, c = 3 x 10^8 m/s Average distance between Sun and Earth, d = 1.5 x 10^8 km = 1.5 x 10^11 m

Time taken by light to travel from the Sun to the Earth, t = d/c t = (1.5 x 10^11 m) / (3 x 10^8 m/s) t ≈ 500 seconds or 8 minutes and 20 seconds

Reflection and Refraction:

Solution:

Given: Refractive index of glass, n = 1.5 Angle of incidence, i = 45 degrees

Using Snell’s law: sin r / sin i = n2 / n1 sin r / sin 45 = 1.5 / 1 sin r = 1.5 * sin 45 sin r ≈ 1.06 r ≈ 41.8 degrees

Angle of reflection, r = Angle of incidence, i = 45 degrees

Lenses:

Solution:

Given: Focal length of the converging lens, f = 10 cm = 0.1 m Object distance, u = 20 cm = 0.2 m

Magnification, m = -v/u m = - (f/d) m = - (0.1 m) / (0.2 m) = -0.5

Prism:

Solution:

Given: Refractive index of prism, n = 1.5 Angle of incidence, i = 60 degrees

Angle of deviation, δ = (n - 1) * A δ = (1.5 - 1) * 60 δ = 0.5 * 60 δ = 30 degrees

Photoelectric Effect:

Solution:

Given: Threshold wavelength, λ0 = 500 nm = 5 x 10^-7 m Wavelength of incident light, λ = 400 nm = 4 x 10^-7 m

Maximum kinetic energy of photoelectrons, Kmax = hc / λ - hc / λ0 Kmax = (6.626 x 10^-34 J s) * (3 x 10^8 m/s) * (1/4 x 10^-7 m - 1/5 x 10^-7 m) Kmax ≈ 1.08 x 10^-19 J

Light Emission:

Solution:

Given: Wavelength of light emitted, λ = 656 nm = 6.56 x 10^-7 m Energy levels: n1 = 2, n2 = 3

Frequency of photon, f = c / λ f = (3 x 10^8 m/s) / (6.56 x 10^-7 m) f ≈ 4.57 x 10^14 Hz

Energy of photon, E = hf E = (6.626 x 10^-34 J s) * (4.57 x 10^14 Hz) E ≈ 3.03 x 10^-19 J

Wave-Particle Duality:

Solution:

Given: Momentum of photon, p = 6.626 x 10^-34 kg m/s

Wavelength of photon, λ = h/p λ = (6.626 x 10^-34 J s) / (6.626 x 10^-34 kg m/s) λ = 1 meter

Polarization:

Solution:

Given: Intensity of original light beam, I0 = 100 W/m^2

Intensity of transmitted light, I = I0 * cos^2 θ I = 100 W/m^2 * (cos 90)^2 I = 100 W/m^2 * 0 I = 0 W/m^2

Since the polarizing filter transmits only vertically polarized light, and the original light beam is unpolarized, the intensity of the transmitted light becomes zero.

CBSE Board Exam Questions:

1. What are the different theories of light?

   • Corpuscular Theory: Proposed by Isaac Newton, this theory suggests that light is made up of tiny particles or corpuscles.

2. Explain the phenomenon of reflection of light.

   • Reflection is the bouncing back of light rays from a surface without any change in frequency.
   • The law of reflection states that the angle of incidence is equal to the angle of reflection, and both angles are measured with respect to the normal at the point of incidence.

3. Derive the laws of refraction of light.

   • Snell’s Law: sin i / sin r = n2 / n1, where i is the angle of incidence, r is the angle of refraction, n1 is the refractive index of the first medium, and n2 is the refractive index of the second medium.

4. Explain the working principle of a lens.

   • A lens is a transparent optical device that converges (convex lens) or diverges (concave lens) light rays.
   • Lenses are used in various optical instruments such as cameras, microscopes, and telescopes.

5. State and explain Huygen’s principle of secondary wavelets.

   • Huygen’s principle states that every point on a wavefront can be considered as a source of secondary wavelets that spread out in all directions.
   • The envelope of these secondary wavelets determines the new wavefront.

6. Explain the phenomenon of interference of light.

   • Interference is the phenomenon of combining two or more waves to produce a new wave with a different amplitude.
   • Constructive interference occurs when the waves are in phase, resulting in a brighter region, while destructive interference occurs when they are out of phase, resulting in a darker region.

7. Explain the phenomenon of diffraction of light.

   • Diffraction is the spreading out of light waves around an obstacle or through a narrow slit.
   • Diffraction is responsible for the formation of patterns such as fringes and halos around light sources.

8. State and explain the laws of blackbody radiation.

   • Planck’s law: The energy radiated by a blackbody is proportional to the fourth power of its absolute temperature.
   • Stefan-Boltzmann law: The total energy radiated by a blackbody is proportional to the fourth power of its absolute temperature.

9. Explain the photoelectric effect.

   • The photoelectric effect is the emission of electrons from a metal surface when exposed to light of sufficient energy (frequency).
   • The kinetic energy of the emitted electrons is proportional to the frequency of the incident light.

10. Explain the principle of the working of a solar cell.

    • A solar cell is a photovoltaic (PV) device that converts light energy directly into electrical energy through the photovoltaic effect.
    • When sunlight strikes the semiconductor material in a solar cell, it creates an electrical current.