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Physics M.C.Q (1 Marks)

Dispersion and Spectra · Rajasthan Board (RBSE) STD 12 Science (Rajasthan - English Medium). 10 questions.

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M.C.Q (1 Marks)

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10 questions · 1 auto-graded MCQ + 9 self-marked written.

Question 11 Mark
The angular dispersion produced by a prism:
  1. Increases if the average refractive index increases.
  2. Increases if the average refractive index decreases.
  3. Remains constant whether the average refractive index increases or decreases.
  4. Has no relation with average refractive index.
Answer
  1. Increases if the average refractive index increases.
Explanation:
If $\mu$ is the average refractive index and A is the angle of prism, then the angular dispersion produced by the prism is given by $\delta=(\mu-1)\text{A}.$
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Question 21 Mark
Which of the following quantities increase when wavelength is increased? Consider only the magnitudes.
  1. The power of a converging lens.
  2. The focal length of a converging lens.
  3. The power of a diverging lens.
  4. The focal length of a diverging lens.
Answer
  1. The focal length of a converging lens.
  1. The focal length of a diverging lens.
Explanation:
The focal length of a lens is inversely proportional to the refractive index of the lens and the refractive index of the lens is inversely proportional to the square of wavelength. Therefore, the focal length is directly dependent on wavelength; it increases when the wavelength is increased.
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Question 31 Mark
Which of the following quantities related to a lens depend on the wavelength or wavelengths of the incident light?
  1. Power.
  2. Focal length.
  3. Chromatic aberration.
  4. Radii of curvature.
Answer
  1. Power.
  2. Focal length.
  3. Chromatic aberration.
Explanation:
The focal length, power and chromatic aberration are dependent on the refractive index of the lens, which itself is dependent on the wavelength of the light.
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Question 41 Mark
By properly combining two prisms made of different materials, it is possible to:
  1. Have dispersion without average deviation.
  2. Have deviation without dispersion.
  3. Have both dispersion and average deviation.
  4. Have neither dispersion nor average deviation.
Answer
  1. ​​​​​​Have dispersion without average deviation.
  2. Have deviation without dispersion.
  3. Have both dispersion and average deviation.
Explanation:
Consider the case of prisms combined such that the refractive angles are reversed w.r.t. each other. Then, the net deviation of the yellow ray will be,
$\delta_\text{y}=(\mu_\text{y}-1)\text{A}-(\mu_\text{y}'-1)\text{A}'$
And, the net angular dispersion will be
$\delta_\text{y}-\delta_\text{r}=(\mu_\text{y}-1)\text{A}(\omega-\omega')$
Thus, by choosing appropriate conditions, we can have the above mentioned cases.
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Question 51 Mark
If a glass prism is dipped in water, its dispersive power:
  1. Increases.
  2. Decreases.
  3. Does not change.
  4. May increase or decrease depending on whether the angle of the prism is less than or greater than 60°.
Answer
  1. Decreases.
Explanation:
If $\mu$ is the refractive index and A is the angle of prism, then the angular dispersion produced by the prism will be given by $\delta=(\mu-1)\text{A}.$
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.
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Question 61 Mark
In producing a pure spectrum, the incident light is passed through a narrow slit placed in the focal plane of an achromatic lens because a narrow slit:
  1. Produces less diffraction.
  2. Increases intensity.
  3. Allows only one colour at a time.
  4. Allows a more parallel beam when it passes through the lens.
Answer
  1. ​​​​​​Allows a more parallel beam when it passes through the lens.
Explanation:
To produce a pure spectrum, a parallel light beam is required to be incident on the dispersing element. So, the incident light is passed through a narrow slit placed in the focal plane of an achromatic lens.
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Question 71 Mark
A narrow beam of white light goes through a slab having parallel faces.
  1. The light never splits in different colours.
  2. The emergent beam is white.
  3. The light inside the slab is split into different colours.
  4. The light inside the slab is white.
Answer
  1. The emergent beam is white.
  2. The light inside the slab is split into different colours.
Explanation:
White light will split into different colours inside the glass slab because the value of refractive index is different for different wavelengths of light; thus, they suffer different deviations. But the emergent light will be white light. As the faces of the glass slide are parallel, the emerging lights of different wavelengths will reunite after refraction.
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MCQ 81 Mark
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
    $f_v - f_r$
  • ✓
    $f_v < f_r$
  • D
    Any of the three is possible depending on the value of the average refractive index $\mu.$
Answer
Correct option: 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 :
$\text{f}\propto\frac{1}{\lambda^2}\ \ (\because\lambda_\text{r}<\lambda_\upsilon)$
$\therefore\text{f}_\text{v}<\text{f}_\text{r}$
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Question 91 Mark
Consider the following two statements:
  1. Line spectra contain information about atoms.
  2. Band spectra contain information about molecules.
  1. Both A and B are wrong
  2. A is correct but B is wrong.
  3. B is correct but A is wrong
  4. Both A and B are correct.
Answer
  1. Both A and B are correct.
Explanation:
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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Question 101 Mark
prism can produce a minimum deviation $\delta$ in a light beam. If three such prisms are combined, the minimum deviation that can be produced in this beam is:
  1. $0$
  2. $\delta$
  3. $2\delta$
  4. $3\delta$
Answer
  1. $\delta$
Explanation:
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.
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