Question 57: Wave Optics

Question

A telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength 500 nm , at a resolution of $5 	imes 10^{-7}$ radian. The value of $R$ is
$\_\_\_\_$ cm .

Accepted Answer

When a plane wave-front (parallel rays) enters a prism, all parts of the wave-front travel at the same speed through the medium. While the wave-front is tilted due to refraction, it remains flat and parallel, thus remaining a plane wave.
According to Huygens' Principle, every point on a wave-front acts as a source of secondary spherical wavelets. When a plane wave encounters a very small opening (pinhole) comparable to the wavelength of light, it undergoes diffraction. The emerging light spreads out in all directions, forming a spherical wave-front.
Hence, the statement I is true.
When light passes through a slit, the degree of spreading (diffraction) depends on the slit width (d) relative to the wavelength ( $\lambda$ ).
Smaller slit widths lead to greater diffraction and more pronounced curvature. As the slit width increases, the light behaves more like a straight beam, meaning the wave-front becomes flatter.
Curvature is the reciprocal of the radius of the wave-front, i.e., $\propto \frac{1}{\mathrm{r}}$. So, a flatter wave has less curvature. Therefore, increasing the slit width decreases the curvature, it does not increase it.
Hence, the statement II is false.
Since Statement I is true and Statement II is false, so the correct option is (C).

Answer

61

Answer

122

Answer

244

Answer

305

Wave Optics

A telescope with objective diameter R is used to observe a distant star emitting light of wavelength 500 nm , at a resolution of 5 \times 10^{-7} radian. The value of R is \_\_\_\_ cm .

Choose the correct answer: