20: Dispersion And Spectra : Neet-xii-physics

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NEET-XII-Physics

20: dispersion and Spectra

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Section : i

Qstn #1
The equation
ω=μu-μrμ-1was derived for a prism having small refracting angle. Is it also valid for a prism of large refracting angle? Is it also valid for a glass slab or a glass sphere?
Ans : Dispersive power depends on angular deviation, and angular deviation is valid only for a small refracting angle and a small angle of incidence. Therefore, dispersive power is not valid for a prism of large refracting angle. It is also not valid for a glass slab or a glass sphere, as it has a large refracting angle.
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Qstn #2
Can the dispersive power
ω=μu-μrμ-1be negative? What is the sign of ω if a hollow prism is immersed into water?
Ans : No, it cannot be negative, as the refractive index for violet light is always greater than that for red light. Also, refractive index is inversely proportional to `` {\lambda }^{2}``. The sign of ω will be positive, as `` \mu `` is still greater than 1 and as `` {\mu }_{v}>{\mu }_{r}``.
Page No 441:

Qstn #3
If three identical prisms are combined, is it possible to pass a beam that emerges undeviated? Undispersed?
Ans : No, it is not possible even when prisms are be combined with their refractive angle reversed with respect to each other. There will be at least a net deviation and dispersion equal to the dispersion and deviation produced by a single prism.
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Qstn #4
“Monochromatic light should be used to produce pure spectrum”. Comment on this statement.
Ans : No, monochromatic light cannot be used to produce a pure spectrum. A spectrum is produced when a light of different wavelengths is deviated through different angles and gets separated. Monochromatic light, on the other hand, has a single wavelength.
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Qstn #5
Does focal length of a lens depend on the colour of the light used? Does focal length of a mirror depend on the colour?
Ans : Yes, the focal length of a lens depends on the colour of light.
According to lens-maker's formula,
`` \frac{1}{f}=(\mu -1)(\frac{1}{{R}_{1}}-\frac{1}{{R}_{2}})``
Here, f is the focal length, μ is the refractive index, R is the radius of curvature of lens.
The refractive index (μ) depends on the inverse of square of wavelength.
The focal length of a mirror is independent of the colour of light.
Page No 441:

Qstn #6
Suggest a method to produce a rainbow in your house.
Ans : A rainbow can be produced using a prism. Another way of producing a rainbow is to dip a mirror inside water, keeping it inclined along the wall of a tumbler. The light coming from water after reflecting from the mirror will give a rainbow.
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Section : ii

Qstn #1
The angular dispersion produced by a prism
(a) increases if the average refractive index increases
(b) increases if the average refractive index decreases
(c) remains constant whether the average refractive index increases or decreases
(d) has no relation with average refractive index
digAnsr: a
Ans : (a) increases if the average refractive index increases
If μ is the average refractive index and A is the angle of prism, then the angular dispersion produced by the prism is given by `` \delta =(\mu -1)A``.

Qstn #2
If a glass prism is dipped in water, its dispersive power
(a) increases
(b) decreases
(c) does not change
(d) may increase or decrease depending on whether the angle of the prism is less than or greater than 60°
digAnsr: b
Ans : (b) decreases
If μ is the refractive index and A is the angle of prism, then the angular dispersion produced by the prism will be given by `` \delta =(\mu -1)A``.
Because the relative refractive index of glass with respect to water is small compared to the refractive of glass with respect to air, the dispersive power of the glass prism is more in air than that in water.
Page No 442:

Qstn #3
A prism can produce a minimum deviation δ in a light beam. If three such prisms are combined, the minimum deviation that can be produced in this beam is
(a) 0
(b) δ
(c) 2δ
(d) 3δ
digAnsr: b
Ans : (b) δ
In combination (refractive angles of prisms reversed with respect to each other), the deviations through two prisms cancel out each other and the net deviation is due to the third prism only.
Page No 442:

Qstn #4
Consider the following two statements :
(A) Line spectra contain information about atoms.
(B) Band spectra contain information about molecules.
(a) Both A and B are wrong
(b) A is correct but B is wrong
(c) B is correct but A is wrong
(d) Both A and B are correct
digAnsr: d
Ans : (d) Both A and B are correct.
Because line spectra contain wavelengths that are absorbed by atoms and band spectra contain bunch wavelengths that are absorbed by molecules, both statements are correct.
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Qstn #5
The focal length of a converging lens are f_v and f_r for violet and red light respectively.
(a) f_v > f_r
(b) f_v = f_r
(c) f_v < f_r
(d) Any of the three is possible depending on the value of the average refractive index μ.
digAnsr: c
Ans : (c) f_v < f_r
Focal length is inversely proportional to refractive index and refractive index is inversely proportional to `` {\lambda }^{2}``. So, keeping other parameters the same, we can say:
`` f\propto \frac{1}{{\lambda }^{2}}(\because {\lambda }_{r}<{\lambda }_{v})``
`` ``
∴ f_v < f_r
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Section : iii