In a given direction, the intensities of the scattered light by a scattering substance for two beams of light are in the ratio of 256 : 81. The ratio of the frequency of the first beam to the frequency of the second beam is

• 64 : 127

• 1 : 2

• 64 : 27

• None of these

Wavelength of given light waves in air and in a medium are 6000 $\stackrel{\circ }{\mathrm{A}}$ and 4000 $\stackrel{\circ }{\mathrm{A}}$ respectively. The critical angle is

• ${\tan }^{-1} \left(\frac{2}{3}\right)$

• ${\tan }^{-1} \left(\frac{3}{2}\right)$

• ${\sin }^{-1} \left(\frac{2}{3}\right)$

• ${\sin }^{-1} \left(\frac{3}{2}\right)$

The time required for the light to pass through a glass slab (refractive index = 1.5) of thickness 4 mm is (c = 3 x 10⁸ ms^-1, speed of light in free space)

• 10^-11 s

• 2 × 10^-11 s

• 2 × 10¹¹ s

• 2 × 10^-5 s

A prism having refractive index 1.414 and refracting angle 30° has one of the refracting surfaces silvered. A beam of light incident on the other refracting surface will retrace its path, if the angle of incidence is

• 0°

• 30°

• 60°

• 45°

135.

A planoconvex lens has a maximum thickness of 6 cm. When placed on a horizontal table with the curved surface in contact with the table surface, the apparent depth of the bottom most point of the lens is found to be 4 cm. If the lens is inverted such that the plane face of the lens is in contact with the surface of the table, the apparent depth of the centre of the plane face is found to be $\left(\frac{17}{4}\right)$ cm. The radius of curvature of the lens is

• 68 cm

• 75 cm

• 128 cm

• 34 cm

Two thin lenses have a combined power of +9D. When they are separated by a distance of 20 cm, their equivalent power becomes $+ \frac{27}{5} \mathrm{D}$. Their individual powers (in dioptre) are

• 1, 8

• 2, 7

• 3, 6

• 4, 5

If the scattering intensity of a liquid is 8 units at a wavelength of 500 nm, then the scattering intensity at a wavelength of 400 nm will be approximately

• 13 units

• 16 units

• 20 units

• 24 units

A point source of light is kept below the surface of water (n_w = 4 /3) at a depth $\sqrt{7}$ m. The radius of the circular bright patch of light noticed on the surface of water is

• $\sqrt{7} \mathrm{m}$

• $\frac{3}{\sqrt{7}} \mathrm{m}$

• 3 m

• $\frac{\sqrt{7}}{3} \mathrm{m}$

Spectrum of sunlight is an example for

• continuous absorption spectrum

• band emission spectrum

• line absorption spectrum

• continuous emission spectrum

Frequencies of light incident on a system of scattering particles are in the ratio of 1 : 2. Then, the intensity of scattered light in a particular directions is

• 1 : 16

• 1 : 4

• 1 : 2

• 1 : 8