41.

If θ1 and θ2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by

• cot²θ = cot²θ₁+ cot²θ₂

• tan₂θ = tan²θ₁+ tan²θ₂

• cot²θ = cot²θ₁– cot²θ₂

• cot²θ = cot²θ₁– cot²θ₂

The ratio of resolving powers of an optical microscope for two wavelengths λ₁ = 4000 Å and λ₂ = 6000 Å is

• 8 : 27

• 9:4

• 3:2

• 3:2

Two Polaroids P₁ and P₂ are placed with their axis perpendicular to each other. Unpolarised light I0 is incident on P₁. A third polaroid P₃
is kept in between P₁ and P₂ such that its axis makes an angle 45^o with that of P₁. The intensity of transmitted light through P₂ is

• I₀/2

• I₀/3

• I₀/8

• I₀/8

A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle θ, the spot of the light is found to move through a distance y on the scale. The angle θ is given by

• y/2x

• y/x

• 2y/x

• 2y/x

A thin prism having refracting angle 10° is made of glass of refractive index 1.42. This prism is combined with another thin prism of a glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be

• 4°

• 6°

• 8°

• 8°