M.C.Q (1 Marks)

MCQ 11 Mark

Which of the following quantities increase when wavelength is increased? Consider only the magnitudes.

The power of a converging lens.
The focal length of a converging lens.
The power of a diverging lens.
The focal length of a diverging lens.

A
Only $A$
B
$A$ and $B$
✓
$B$ and $D$
D
$C$ and $D$

Answer

Correct option: C.

$B$ and $D$

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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MCQ 21 Mark

Which of the following quantities related to a lens depend on the wavelength or wavelengths of the incident light?

A
Power.
B
Focal length.
C
Chromatic aberration.
✓
All of the above

Answer

Correct option: D.

All of the above

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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MCQ 31 Mark

By properly combining two prisms made of different materials, it is possible to:

A
Have dispersion without average deviation.
B
Have deviation without dispersion.
C
Have both dispersion and average deviation.
✓
All of the above

Answer

Correct option: D.

All of the above

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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MCQ 41 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:

A
$0$
✓
$\delta$
C
$2\delta$
D
$3\delta$

Answer

Correct option: B.

$\delta$

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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MCQ 51 Mark

If a glass prism is dipped in water, its dispersive power:

A
Increases.
✓
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°.

Answer

Correct option: B.

Decreases.

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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MCQ 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:

A
Produces less diffraction.
B
Increases intensity.
C
Allows only one colour at a time.
✓
Allows a more parallel beam when it passes through the lens.

Answer

Correct option: D.

Allows a more parallel beam when it passes through the lens.

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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MCQ 71 Mark

The angular dispersion produced by a prism:

✓
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.

Answer

Correct option: A.

Increases if the average refractive index increases.

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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MCQ 81 Mark

A narrow beam of white light goes through a slab having parallel faces.

The light never splits in different colours.
The emergent beam is white.
The light inside the slab is split into different colours.
The light inside the slab is white.

A
Only $A$
B
$A$ and $B$
✓
$B$ and $C$
D
None of these

Answer

Correct option: C.

$B$ and $C$

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 91 Mark

Consider the following two statements:
$A.$ Line spectra contain information about atoms.
$B.\ B$ and 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
✓
Both $A$ and $B$ are correct.

Answer

Correct option: 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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MCQ 101 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
$f_v-f_{\mathrm{r}}$
✓
$f_v<f_r$
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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Physics M.C.Q (1 Marks)

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