CBSE Class 12 Physics Chapter 19 Wave Optics NCERT Solutions

Given:

Wavelength of incident monochromatic light, \lambda = 589 \text{ nm} = 589 \times 10^{-9} \text{ m}

Speed of light in air, c = 3 \times 10^8 \text{ m/s}

Refractive index of water, \mu = 1.33

First, let's calculate the frequency of the incident light, as frequency remains constant regardless of the medium.

Frequency v = \frac{c}{\lambda} = \frac{3 \times 10^8 \text{ m/s}}{589 \times 10^{-9} \text{ m}} \approx 5.09 \times 10^{14} \text{ Hz}

(a) Reflected light:

When light is reflected from a surface, it bounces back into the same medium. Therefore, the properties of the reflected light are the same as the incident light.

• Speed: The speed of the reflected light is the same as the speed of light in air, which is $3\; \backslash times\; 10^8\; \backslash text\{\; m/s\}$.
• Frequency: The frequency of the reflected light is the same as the incident light, which is approximately $5.09\; \backslash times\; 10^\{14\}\; \backslash text\{\; Hz\}$.
• Wavelength: The wavelength of the reflected light is the same as the incident light, which is $589\; \backslash text\{\; nm\}$.

Hence, for the reflected light: Speed = $3\; \backslash times\; 10^8\; \backslash text\{\; m/s\}$, Frequency = $5.09\; \backslash times\; 10^\{14\}\; \backslash text\{\; Hz\}$, Wavelength = $589\; \backslash text\{\; nm\}$.

(b) Refracted light:

When light is refracted, it enters a different medium. The frequency of light does not change when it passes from one medium to another.

• Frequency: The frequency of the refracted light is the same as the incident light, which is approximately $5.09\; \backslash times\; 10^\{14\}\; \backslash text\{\; Hz\}$.
• Speed: The speed of light in water can be calculated using the refractive index: $v\; =\; \backslash frac\{c\}\{\backslash mu\}\; =\; \backslash frac\{3\; \backslash times\; 10^8\; \backslash text\{\; m/s\}\}\{1.33\}\; \backslash approx\; 2.26\; \backslash times\; 10^8\; \backslash text\{\; m/s\}$.
• Wavelength: The wavelength of light in water can be calculated using its speed and frequency: $\backslash lambda\_\{\backslash text\{water\}\}\; =\; \backslash frac\{v\}\{v\}\; =\; \backslash frac\{2.26\; \backslash times\; 10^8\; \backslash text\{\; m/s\}\}\{5.09\; \backslash times\; 10^\{14\}\; \backslash text\{\; Hz\}\}\; \backslash approx\; 4.44\; \backslash times\; 10^\{-7\}\; \backslash text\{\; m\}\; =\; 444\; \backslash text\{\; nm\}$.

Hence, for the refracted light: Speed = $2.26\; \backslash times\; 10^8\; \backslash text\{\; m/s\}$, Frequency = $5.09\; \backslash times\; 10^\{14\}\; \backslash text\{\; Hz\}$, Wavelength = $444\; \backslash text\{\; nm\}$.

The shape of a wavefront depends on the nature and position of the source of light.

(i) Light diverging from a point source:

When light originates from a point source, it spreads out in all directions equally. The locus of points where the light disturbance has the same phase forms a spherical surface. Therefore, the wavefront is spherical.

(ii) Light emerging out of a convex lens when a point source is placed at its focus:

When a point source is placed at the principal focus of a convex lens, the rays of light emerging from the lens become parallel to the principal axis. A collection of parallel rays constitutes a plane wavefront. Therefore, the wavefront is plane.

(iii) The portion of the wavefront of light from a distant star intercepted by the Earth:

Light from very distant sources, such as stars, travels over immense distances. Even though the wavefront originating from the star is spherical, the radius of curvature is extremely large. Over the small area intercepted by the Earth, this large spherical wavefront can be approximated as a plane wavefront.