A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If ${\rm{\mu }}$ is the refractive index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is

${\cos ^{ - 1}}\,\,\left( {\frac{1}{{\rm{\mu }}}} \right)$

${\sin ^{ - 1}}\,\,\left( {\frac{1}{{\rm{\mu }}}} \right)$

${\tan ^{ - 1}}\,\,\left( {\frac{1}{{\rm{\mu }}}} \right)$

${\sin ^{ - 1}}\,\,\left( {\frac{{{\rm{\mu }} - 1}}{{\rm{\mu }}}} \right)$

An astronomical telescope has an angular magnification of magnitude ${\rm{5}}$ for distant objects. The separation between the objective and the eye-piece is ${\rm{36}}\,\,{\rm{cm}}$ and the final image is formed at infinity. The focal length ${f_0}$ of the objective and the focal length ${f_e}$ of the eye-piece are

${f_0} = 30\;\,{\rm{cm\;and\;}}\,{f_e} = 6\,\;{\rm{cm}}$

${f_0} = 45\;\,{\rm{cm\;and\;}}\,{f_e} = - \,9\,\;{\rm{cm}}$

${f_0} = - 7.2\;\,{\rm{cm\;and\;}}\,{f_e} = 5\;\,{\rm{cm}}$

${f_0} = 50\,\;{\rm{cm\;and\;}}\,{f_e} = 10\;\,{\rm{cm}}$

A person cannot see properly beyond ${\rm{2}}\,\,{\rm{m}}$. Power of the lens is

${\rm{ - 0}}{\rm{.5}}\,\,{\rm{D}}$

${\rm{0}}{\rm{.5}}\,\,{\rm{D}}$

${\rm{1}}{\rm{.5}}\,\,{\rm{D}}$

${\rm{ - 2}}{\rm{.5}}\,\,{\rm{D}}$

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Ray optics practice · Mixed difficulty

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Showing 1-30 of 249 questions

1 Medium

1 of 249

Application +4 | -1

An object 5 cm tall is placed

\mathrm{1}\,\,\mathrm{m}

from a concave spherical mirror which has a radius of curvature of

\mathrm{20}\,\,\,\mathrm{cm}

. The size of the image is

View answer and explanation

Correct option: C

\mathrm{0}\mathrm{.55}\,\,\mathrm{cm}

Option C (

\mathrm{0}\mathrm{.55}\,\mathrm{cm}

) is correct because the size of the image is calculated using the magnification formula for a concave mirror.

2 Medium

2 of 249

Understanding +4 | -1

Red colour is used for danger signals because

View answer and explanation

Correct option: B

It undergoes least scattering

Option B (It undergoes least scattering) is correct because red light has the longest wavelength and is scattered the least by atmospheric particles, making it visible from a greater distance.

3 Medium

3 of 249

Analyzing +4 | -1

A ray of light is incident on the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If

\mathrm{\mu }

is the refractive index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is

View answer and explanation

Correct option: D

{\cos ^{ - 1}}\,\,\left( {\frac{1}{\mathrm{\mu }}} \right)

Option D (

{\cos ^{ - 1}}\,\left( {\frac{1}{\mathrm{\mu }}} \right)

) is correct because it represents the maximum base angle for total internal reflection to occur at the hypotenuse.

4 Medium

4 of 249

Analyzing +4 | -1

Statement-A: The minimum distance between an object and its real image formed by a convex lens is

2{f}

.

Statement-B: The distance between an object and its real image is minimum when its magnification is -1.

View answer and explanation

Correct option: D

A is wrong and B is correct

Option D (A is wrong and B is correct) is correct because the minimum distance between an object and its real image formed by a convex lens is 4f, and this occurs when the magnification is -1.

5 Medium

5 of 249

Analyzing +4 | -1

Assertion: We cannot produce a real image by plane or convex mirrors under any circumstances.
Reason: The focal length of a convex mirror is always taken negative.

View answer and explanation

Correct option: D

If both Assertion and Reason are false

Option D (If both Assertion and Reason are false) is correct because both statements are incorrect. Real images can be formed by concave mirrors, and the focal length of a convex mirror is positive.

6 Medium

6 of 249

Remembering +4 | -1

If both the object and image are at infinite distance from a refracting telescope its magnifying power will be equal to

View answer and explanation

Correct option: C

The ratio of the focal length of the objective and eyepiece

Option C (The ratio of the focal length of the objective and eyepiece) is correct because the magnifying power of a refracting telescope is the ratio of the objective's focal length to the eyepiece's focal length.

7 Medium

7 of 249

Analyzing +4 | -1

Assertion (A): In Snell's law

\mu=\frac{\sin i}{\sin r}

, angle

i

is always angle of incidence.

Reason (R):

\mu=\frac{\sin i}{\sin r}

is applicable one medium in air (or vacuum).

View answer and explanation

Correct option: C

If assertion is true but reason is false.

Option C (If assertion is true but reason is false) is correct because Snell's law applies to any two media, not just air or vacuum.

8 Medium

8 of 249

Application +4 | -1

Two thin lenses, one of focal length

+ \,60\,\,cm

and the other of focal length

- \,20\,\,cm

are put in contact. The combined focal length is

View answer and explanation

Correct option: D

- \,30\,\,cm

Option D (

\ - \,30\,\,cm

) is correct because it is calculated using the formula for the combined focal length of two lenses in contact.

9 Medium

9 of 249

Understanding +4 | -1

A liquid wets a solid. The meniscus of the liquid in a long vertical capillary tube of that solid is

View answer and explanation

Correct option: B

Concave upward

Option B (Concave upward) is correct because a liquid that wets a solid has adhesive forces greater than cohesive forces, causing the liquid to rise and form a concave meniscus.

10 Medium

10 of 249

Remembering +4 | -1

Which of the following colours suffers maximum deviation in a prism

View answer and explanation

Correct option: B

Blue

Option B (Blue) is correct because blue light has a shorter wavelength and experiences greater deviation in a prism.

11 Hard

11 of 249

Application +4 | -1

The diameter of objective lens of a telescope is

6 \mathrm{~cm}

and wavelength of light used is

540 \mathrm{~nm}.

The resolving power of telescope is

View answer and explanation

Correct option: A

9.1 \times 10^4 \mathrm{~rad}^{-1}

Option A (

9.1 \times 10^4 \mathrm{~rad}^{-1}

) is correct. Resolving power is calculated using the formula

1.22 \frac{\lambda}{D}

and then taking the reciprocal.

12 Medium

12 of 249

Application +4 | -1

An astronomical telescope has an angular magnification of magnitude 5 for distant objects. The separation between the objective and the eyepiece is 36 cm. The final image is formed at infinity. The focal lengths

{f_0}

of the objective and

{f_e}

of the eyepiece are

View answer and explanation

Correct option: D

30 cm and 6 cm respectively

Option D (30 cm and 6 cm respectively) is correct because the angular magnification is the ratio of the focal lengths, and the separation is the sum of the focal lengths when the final image is at infinity.

13 Medium

13 of 249

Remembering +4 | -1

The refractive index of a piece of transparent quartz is the greatest for

View answer and explanation

Correct option: B

Violet light

Option B (Violet light) is correct because the refractive index is inversely proportional to the wavelength of light, and violet light has the shortest wavelength.

14 Medium

14 of 249

Application +4 | -1

An astronomical telescope has an angular magnification of magnitude

\mathrm{5}

for distant objects. The separation between the objective and the eye-piece is

\mathrm{36}\,\,\mathrm{cm}

and the final image is formed at infinity. The focal length

{f_0}

of the objective and the focal length

{f_e}

of the eye-piece are

View answer and explanation

Correct option: D

{f_0} = 30\;\,\mathrm{cm\;and\;}\,{f_e} = 6\,\;\mathrm{cm}

Option D (

{f_0} = 30\;\,\mathrm{cm\;and\;}\,{f_e} = 6\;\,\mathrm{cm}

) is correct because it satisfies both the angular magnification and the separation conditions for an astronomical telescope.

15 Medium

15 of 249

Understanding +4 | -1

When light enters water from the vacuum, then the wavelength of light

View answer and explanation

Correct option: A

Decreases

Option A is correct because when light enters a medium with a higher refractive index (like water from a vacuum), its speed decreases, and since the frequency remains constant, the wavelength must decrease.

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16 Medium

16 of 249

Analyzing +4 | -1

A short straight object of height 100 cm lies before the central axis of a spherical mirror, whose focal length has absolute value

f = 40\,cm

. The image of object produced by the mirror is of height 25 cm and has the same orientation of the object. One may conclude from the information.

View answer and explanation

Correct option: D

Image is virtual, opposite side of convex mirror

Option D (Image is virtual, opposite side of convex mirror) is correct because a convex mirror always produces virtual, erect, and diminished images.

17 Medium

17 of 249

Application +4 | -1

In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:

View answer and explanation

Correct option: A

27.5 cm

Option A (27.5 cm) is correct because the object and image coincide when the ray retraces its path, indicating the object is at the center of curvature of the mirror.

18 Medium

18 of 249

Application +4 | -1

. An movie projector forms an image

3.5\,\,m

long of an object

35\,\,mm

. Supposing there is negligible absorption of light by aperture then illuminance on slide and screen will be in the ratio of

View answer and explanation

Correct option: B

{10^4}:1

Option B (

{10^4}:1

) is correct because the illuminance is inversely proportional to the square of the image size (or the square of the magnification).

19 Medium

19 of 249

Analyzing +4 | -1

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The phase difference of two light waves change if they travel through different media having same thickness, but different indices of refraction.

Reason R: The wavelengths of waves are different in different media.

In the light of the above statements, choose the most appropriate answer from the options given below

View answer and explanation

Correct option: D

Both A and R are correct and R is the correct explanation of A

Option D (Both A and R are correct and R is the correct explanation of A) is correct because the phase difference depends on the wavelength, which changes in different media.

20 Easy

20 of 249

Understanding +4 | -1

The passenger side-view mirror on an automobile often has the notation. "Objects seen in mirror are closer than they appear". Is the image really farther away than the object?

View answer and explanation

Correct option: B

No, the image is smaller and closer than the object

Option B is correct because the convex mirror used in the side-view mirror creates a smaller, upright, and virtual image that appears closer than the actual object.

21 Medium

21 of 249

Understanding +4 | -1

The aperture of a telescope is made large, because

View answer and explanation

Correct option: A

To increase the intensity of image

Option A (To increase the intensity of image) is correct because a larger aperture allows more light to enter the telescope, resulting in a brighter and more intense image.

22 Easy

22 of 249

Application +4 | -1

Light of wavelength

500 \mathrm{~nm}

travelling with a speed of

2.0 \times 10^8 \mathrm{~ms}^{-1}

in a certain medium enters another medium of refractive index

5 / 4

times that of the first medium. What are the wavelength and speed in the second medium?

View answer and explanation

Correct option: A

Wavelength/nm - 400, Speed

/\mathrm{ms}^{-1}

1.6 \times 10^8

Option A (Wavelength/nm - 400, Speed

/\mathrm{ms}^{-1}

1.6 \times 10^8

) is correct because both wavelength and speed decrease when light enters a denser medium.

23 Medium

23 of 249

Remembering +4 | -1

The spectrum obtained from an electric lamp or red hot heater is

View answer and explanation

Correct option: D

Continuous spectrum

Option D (Continuous spectrum) is correct because an electric lamp or red hot heater emits light of all wavelengths.

24 Easy

24 of 249

Application +4 | -1

Critical angle of incidence for a pair of optical media is

45^{\circ}

. The refractive indices of first and second media are in the ratio:

View answer and explanation

Correct option: A

\sqrt{2}: 1

Option A (

\sqrt{2}: 1

) is correct because the ratio of refractive indices is inversely proportional to the sine of the critical angle.

25 Easy

25 of 249

Analyzing +4 | -1

Mimimum distance between object and image formed by concave mirror of focal length

f

can be:

View answer and explanation

Correct option: D

zero

Option D (zero) is correct because the minimum distance between an object and its image formed by a concave mirror is zero when the object is at the focal point.

26 Medium

26 of 249

Analyzing +4 | -1

Assertion: In ionospheric reflection, phase change does not occurs with the light wave.
Reason: The ionosphere reflection is similar to the total internal reflection which is similar to the total internal reflection in miraj

View answer and explanation

Correct option: A

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion

Option A (If both Assertion and Reason are correct and Reason is the correct explanation of Assertion) is correct because ionospheric reflection is similar to total internal reflection, and no phase change occurs.

27 Medium

27 of 249

Application +4 | -1

A person cannot see properly beyond

\mathrm{2}\,\,\mathrm{m}

. Power of the lens is

View answer and explanation

Correct option: D

\mathrm{ - 0}\mathrm{.5}\,\,\mathrm{D}

Option D (

\mathrm{ - 0}\mathrm{.5}\,\mathrm{D}

) is correct because a person who cannot see beyond 2m needs a diverging lens with power -0.5 D.

28 Easy

28 of 249

Application +4 | -1

Light enters from air into a given medium at an angle of

45^{\circ}

with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of

15^{\circ}

from its original direction. The refractive index of the medium is

View answer and explanation

Correct option: C

1.414

Option C (

1.414

) is correct because it is calculated using Snell's law, considering the deviation angle.

29 Medium

29 of 249

Understanding +4 | -1

Small vales of numerical aperture (NA) decrease the pulse dispersion but increase losses due to

View answer and explanation

Correct option: D

Microbending

Option C is correct. Small numerical aperture increases losses due to bending because the light is more likely to escape the core when the fiber bends sharply.

30 Medium

30 of 249

Application +4 | -1

Find the luminous intensity of the sun if it produces the same illuminance on the earth as produced by a bulb of

10000\,\,candela

at a distance

0.3\,\,m

. The distance between the sun and the earth is

1.5\,\, \times \,\,{10^{11}}\,\,m

View answer and explanation

Correct option: C

25\,\, \times \,\,{10^{26}}\,\,cd

Option C (

25 \times {10^{26}}\,cd

) is correct because it is calculated by equating the illuminance produced by the sun and the bulb and then solving for the luminous intensity of the sun.

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Key Takeaways

✓ This set contains 249 single-correct-answer MCQs on RAY OPTICS.
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