Appeared in: 2026 (3 sets)
(a) A monochromatic beam of light is travelling from a rarer to a denser medium. Giving reasons, explain the following :
(i) Is the frequency of the reflected and the refracted light the same as the frequency of incident light ?
(ii) Does the decrease in speed in denser medium imply a reduction in the energy carried by the light wave ?
OR
(b) (i) The lower half of a concave mirror's reflecting surface is covered with an opaque non-reflecting material. What effect will this have on the image of an object placed in front of the mirror ?
(ii) A lens made of glass of refractive index $1\cdot5$ disappears, when immersed in a trough of liquid. What is the refractive index of the liquid ?
Give reasons for your answer in each case.
✓ Verified CBSE Marking Scheme
Official Evaluation Steps & EL10 Insight
Solution (a)
(i) Frequency of reflected and refracted light:
- Step 1 (Governing Principle): [0.5 Mark] The frequency of a light wave is a characteristic property of the source of light and does not depend on the medium through which it propagates.
- Step 2 (Reasoning): [0.5 Mark] Since the frequency is determined by the source, it remains unchanged during reflection and refraction. Thus, the frequency of both reflected and refracted light is the same as that of the incident light.
(ii) Energy carried by the light wave:
- Step 1 (Governing Principle): [0.5 Mark] The energy of a light wave is proportional to the square of its amplitude ($E \propto A^2$) and is related to frequency by the Planck-Einstein relation: $$E = h\nu$$
- Step 2 (Reasoning): [0.5 Mark] Since the frequency ($\nu$) remains constant and the energy of a photon depends only on its frequency, the decrease in speed does not imply a reduction in the energy carried by the light wave.
💡 EL10 Concept Insight: Think of light like a marching band; even if they slow down because they hit mud (denser medium), the number of steps they take per minute (frequency) stays exactly the same, so their "energy" per step doesn't change!
Solution (b)
(i) Effect of covering the lower half of a concave mirror:
- Step 1 (Governing Principle): [0.5 Mark] Image formation by a mirror is a collective result of light rays originating from every point of the object and reflecting from every point of the mirror's surface.
- Step 2 (Reasoning): [0.5 Mark] Covering the lower half reduces the intensity (brightness) of the image because fewer rays are reflected, but the size and position of the image remain unchanged as the remaining upper half still forms the complete image.
(ii) Refractive index of the liquid:
- Step 1 (Governing Principle / Lens Maker's Formula): [0.5 Mark] The focal length $f$ of a lens is given by: $$\frac{1}{f} = \left( \frac{\mu_l}{\mu_m} - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$$ Where $\mu_l$ is the refractive index of the lens and $\mu_m$ is the refractive index of the medium.
- Step 2 (Mathematical Working): [0.25 Mark] For the lens to disappear, it must become invisible, meaning its power must become zero ($P = 0$), which implies the focal length $f \to \infty$. $$\frac{1}{f} = 0 \implies \left( \frac{\mu_l}{\mu_m} - 1 \right) = 0$$ $$\frac{\mu_l}{\mu_m} = 1 \implies \mu_m = \mu_l$$
- Step 3 (Final Answer): [0.25 Mark] Given $\mu_l = 1.5$, therefore, the refractive index of the liquid must be $1.5$.
💡 EL10 Concept Insight: If you put a glass lens into a liquid that bends light exactly the same way glass does, the light won't "see" the lens anymore—it just passes straight through as if the lens were invisible