A plane wavefront passes from water (refractive index 4/3) into glass (refractive index 3/2). In the time one edge of the wavefront moves 9 cm in water, a secondary wavelet spreads into the glass from the other edge. The radius of this wavelet is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8 cm
Both distances are covered in the same time \( \tau \), so each is proportional to the speed in its medium. The speed in a medium is \( c/n \).
\( \begin{aligned} BC &= v_1\tau=9\ \mathrm{cm} \\ AE &= v_2\tau \end{aligned} \)
\( \begin{aligned} \frac{AE}{BC} &= \frac{v_2}{v_1} \\ &= \frac{n_1}{n_2} \end{aligned} \)
\( \begin{aligned} AE &= 9\times\frac{4/3}{3/2} \\ &= 9\times\frac{8}{9} \\ &= 8\ \mathrm{cm} \end{aligned} \)
Hence, the secondary wavelet in glass has a radius of 8 cm.
NCERT (2026-27):
Refraction of a plane wave – “… Let τ be the time taken by the wavefront to travel the distance BC. Thus,”
\( \displaystyle BC = v_1\tau \)
Refraction of a plane wave – “… we draw a sphere of radius v2τ from the point A in the second medium … Let CE represent a tangent plane drawn from the point C on to the sphere. Then, AE = v2τ and CE would represent the refracted wavefront. …”
Refraction of a plane wave – “… Now, if c represents the speed of light in vacuum, then,”
\( \displaystyle n_1=\frac{c}{v_1} \)\( \qquad (10.4) \)
“and”
\( \displaystyle n_2=\frac{c}{v_2} \)\( \qquad (10.5) \)
“are known as the refractive indices of medium 1 and medium 2, respectively. …”