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Correct Answer is: (c) R / μ - 1 

From symmetry, the rays must pass through the sphere, parallel to the optic axis.

Using μ₂/v - μ₁/u = μ₂ - μ₁ / r

μ/∞  - 1/u = μ - 1 / R

u = - R / μ - 1.

Correct answer is (D) photons obeying the rules of waves

Correct answer is (B) Only P and Q

We know that, when we use quantum wave plate then a linear polarized beam change circular polarized beam.

t_1/4 = \(\cfrac14\)= \(\cfrac{\lambda}{(H_0-H_e)}\)

where, H₀ = refractive index of ordinary wave

H_e = refractive index of extra ordinary wave.

H₀ - H_e = \(\cfrac{\lambda}{4t_{t/4}}\)

H₀ - H_e = \(\cfrac{6\times10^{-5}}{4\times0.003}\)

H₀ - H_e = \(\cfrac{6\times10^{-2}}{12}\)

H₀ - H_e = 0.5 x 10^-2

For thin prisms (refracting angle < sin 10°).

sin θ ≈ θ

∴ Refractive index, n = \(\frac{sin\,i}{sin\,r_i}\) ≈ \(\frac{i}{r_1}\)

Also n = \(\frac{sin\,e}{sin\,r_2}\) ≈ \(\frac{e}{r_2}\)

∴ i ≈ n r₁ and e ≈ nr₂

ii. Substituting this in, i + e = A + δ, 

we get,

i + e = n (r₁ + r₂) = nA = A + δ

∴ S = A(n – 1)

A and n are constant for a given prism. 

Thus, for a thin prism, for small angles of incidence, angle of deviation is constant (independent of angle of incidence).

(c) 3 

A terrestrial telescope consists of three lenses: 

objective, erecting lens and eyepiece.

A terrestrial telescope has an additional erecting lens to make the final image erect.

The collimator is an arrangement to produce a parallel beam of light.

The spectrometer is an optical instrument used to study the spectra of different sources of light and to measure the refractive indices of materials.

Myopia (or) short sightedness:

It is a vision defect in which a person can see nearby objects clearly but cannot see the distant objects clearly beyond a certain point.

Remedy (correction):

A myopia eye is corrected by using a concave lens of focal length equal to the distance of the far point F from the eye.

Hypermetropia (or) Long sightedness: 

It is a vision defect in which a person can see the distant objects clearly but cannot see the nearby objects clearly. 

Remedy (correction): 

A hypermetropic eye is corrected by using a convex lens of suitable focal length.

This defect is similar to hypermetropia i.e., a person having this defect cannot see nearby objects distinctly, but can see distant objects without any difficulty. This defect occurs in elderly persons (aged persons).

Astigmatism is the defect arising due to different curvatures along different planes in the eye lens. Astigmatic person cannot see all the directions equally well. The defect due to astigmatism is more serious than myopia and hyperopia.

In this defect, eye cannot see parallel and horizontal lines clearly. It may be inherited or acquired. It is due to the imperfect structure of eye lens because of the development of cataract on the lens, ulceration of cornea, injury to the . refracting surfaces, etc. Astigmatism can be corrected by using cylindrical lenses (Torrid lenses).

(b) If both Assertion and reason are true but Reason is not the correct explanation of Assertion.

If the energy of the incident beam of light and the scattered beam of light are same, then it is called as 'elastic scattering'.

When sunlight enters the Earth’s atmosphere, the atoms and molecules of different gases present in the atmosphere refract the light in all possible directions. This is called as ‘Scattering of light’.

If the energy of the incident beam of light and the scattered beam of light are not same, then it is called as 'inelastic scattering'.

1. Elastic scattering

2. Inelastic scattering

The lines are Fraunhofer lines.

(b) If both Assertion and Reason are true but reason is not the correct explanation of Assertion.

The spectral lines which are having frequencies other than the incident ray frequency are called 'Raman lines'.

(a) If both Assertion and Reason are true and Reason is the correct explanation of Assertion

The lines having frequencies lower than the incident frequency is called stokes lines and the lines having frequency higher than the incident frequency are called antistokes lines.

The nature and size of the scatterer results in different types of scattering. 

They are 

1. Rayleigh scattering 

2. Mie scattering 

3. Tyndall scattering 

4. Raman scattering

1. Elaborate view of the Galaxies, Planets, stars and other heavenly bodies is possible. 

2. Camera can be attached for taking photograph for the celestial objects. 

3. Telescope can be viewed even with the low intensity of light.

(a) If both Assertion and Reason are true and Reason is the correct explanation of Assertion.

(a) μ = A + \(\frac{B}{λ^2}\) 

According to cauchy’s relation, (a) μ = A + \(\frac{B}{λ^2}\) 

Primary focus: The primary focus F₁ is defined as a point where an object should be placed to give parallel emergent rays to the principal axis. 

Secondary focus: The secondary focus F₂ is defined as a point where all the parallel rays travelling close to the principal axis converge to form an image on the principal axis.