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

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

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

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

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

Two convex lenses of focal lengths ${\rm{0}}.{\rm{03}}\,\,{\rm{m}}\,\,{\mkern 1mu} {\rm{and}}\,\,{\mkern 1mu} {\rm{0}}.{\rm{05}}\,\,{\rm{m}}$ are used to make a telescope. The distance kept between the two in order to obtain an image at infinity is

${\rm{0}}{\rm{.35}}\,\,{\rm{cm}}$

${\rm{0}}{\rm{.25}}\,\,{\rm{cm}}$

${\rm{0}}{\rm{.175 }}\,{\rm{m}}$

${\rm{0}}{\rm{.15 }}\,{\rm{m}}$

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JEE • PHYSICS • RAY OPTICS

Ray optics practice · Medium

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271 Medium

271 of 443

Application +4 | -1

A convex lens 'A' of focal length 30 cm and a
concave lens 'B' of focal length 10 cm are kept
along the same axis with a distance 'd' between
them. If a parallel beam of light falling on 'A' leaves
'B' as a parallel beam, then the distance 'd' in cm
will be:

View answer and explanation

Correct option: D

Option D (20) is correct because for the beam to remain parallel after passing through both lenses, the focal point of the convex lens must coincide with the focal point of the concave lens.

272 Medium

272 of 443

Analyzing +4 | -1

Assertion: If the rays are diverging after emerging from a lens; the lens must be concave.
Reason: The convex lens can give diverging rays.
In above question a statement of assertion is followed by statement of reason mark the correct choice.

View answer and explanation

Correct option: D

Both assertion and reason are false

Option D is correct because a convex lens can produce diverging rays under certain conditions, and a lens that produces diverging rays is not necessarily concave.

273 Medium

273 of 443

Application +4 | -1

Radius of curvature of concave mirror is

40\,\,cm

and the size of image is twice as that of object, then the object distance is

View answer and explanation

Correct option: D

30\,\,cm

Option D (

30\,\,cm

) is correct because it is the object distance calculated using the mirror formula and the given magnification of 2 for a real image.

274 Medium

274 of 443

Analyzing +4 | -1

Assertion: The cloud in sky generally appear to be whitish.

Reason: Diffraction due to cloud is efficient in equal measure at all wavelengths.

View answer and explanation

Correct option: C

If assertion is true but reason is false.

Option C is correct because the assertion is true, but the reason is false. Clouds appear whitish due to scattering, but diffraction is not equally efficient at all wavelengths.

275 Medium

275 of 443

Understanding +4 | -1

Statement-A: The blue colour of sky is on account of scattering of sun light.

Statement-B: The intensity of scattered light varies inversely as the fourth power of wavelength of the light.

View answer and explanation

Correct option: A

A and B are correct

Option A is correct. The blue color of the sky is due to the scattering of sunlight, and the intensity of scattered light is inversely proportional to the fourth power of the wavelength (Rayleigh scattering).

276 Medium

276 of 443

Understanding +4 | -1

Which of the following statements is correct?

View answer and explanation

Correct option: C

In a spherical mirror, object and its image are always on the same side of focus

Option D (None of the above) is the correct answer because options A, B, and C are not universally true for all cases of mirrors.

277 Medium

277 of 443

Understanding +4 | -1

Assertion: A ray of light incident along the normal to the plane mirror retraces its path after reflection from the mirror.
Reason: A ray of light along the normal has angle of incidence as

\pi / 2

and hence, it retraces its own path after reflection from mirror.

View answer and explanation

Correct option: C

Assertion is true but Reason is false

Option C (Assertion is true but Reason is false) is correct because the angle of incidence for a ray along the normal is 0, not

\pi/2

278 Medium

278 of 443

Understanding +4 | -1

If aperture of lens is halved then image will be

View answer and explanation

Correct option: C

Both

\left( \mathrm{a} \right)\mathrm{ and }\left( \mathrm{b} \right)

Option C (Both (a) and (b)) is correct because halving the aperture reduces the intensity of the image while not affecting its size.

279 Medium

279 of 443

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 across a continuous range of wavelengths, producing a continuous spectrum.

280 Medium

280 of 443

Understanding +4 | -1

A person using a lens as a simple microscope sees an

View answer and explanation

Correct option: C

Upright virtual image

Option C (Upright virtual image) is correct because a simple microscope (convex lens) forms an upright and virtual image when the object is placed within its focal length.

281 Medium

281 of 443

Understanding +4 | -1

The wavelength of light in air and some other medium are respectively

{\lambda _a}

and

{\lambda _m}

. The refractive index of medium is

View answer and explanation

Correct option: A

{\lambda _a}/{\lambda _m}

Option A (

{\lambda _a}/{\lambda _m}

) is correct because the refractive index is the ratio of the wavelength in air to the wavelength in the medium.

282 Medium

282 of 443

Application +4 | -1

The radii of curvature of the faces of a double convex lens are

10 \mathrm{~cm}

and

15 \mathrm{~cm}

. If focal length is

12 \mathrm{~cm}

, what is the refractive index of glass?

View answer and explanation

Correct option: C

\mu=1.5

Option C (

\mu=1.5

) is correct because it is the refractive index calculated using the lens maker's formula with the given radii of curvature and focal length.

283 Medium

283 of 443

Understanding +4 | -1

Statement-I: For observing traffic at our back, we prefer to use a convex mirror.

Statement-II: A convex mirror has a much larger field of view than a plane mirror or a concave mirror.

View answer and explanation

Correct option: A

Both statement-I and statement-II are true

Option A (Both statement-I and statement-II are true) is correct because convex mirrors provide a wider field of view compared to plane or concave mirrors, making them suitable for rear-view mirrors.

284 Medium

284 of 443

Understanding +4 | -1

First and second focal lengths of spherical surface of

n

refractive index are

f_1

and

f_2

respectively. The relation between them, is

View answer and explanation

Correct option: B

f_2= -f_1

Option B is correct because the first and second focal lengths of a spherical surface have equal magnitudes but opposite signs.

285 Medium

285 of 443

Application +4 | -1

The magnifying power of a simple microscope is 6. The focal length of its lens in metres will be, if least distance of distinct vision is 25 cm.

View answer and explanation

Correct option: A

0.05

Option A (0.05) is correct because the focal length is calculated using the magnifying power formula for a simple microscope.

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286 Medium

286 of 443

Understanding +4 | -1

A converging lens is used to form an image on a screen. When upper half of the lens is covered by an opaque screen

View answer and explanation

Correct option: D

Complete image will be formed of decreased intensity

Option D (Complete image will be formed of decreased intensity) is correct because each point on the object reflects light in all directions, and only some of those rays are blocked.

287 Medium

287 of 443

Analyzing +4 | -1

Assertion : Critical angle is maximum for end colour in water air system for visible light.

Reason: Because

\sin \theta_{\mathrm{C}}=\frac{1}{\mu}

and

\mu_{\mathrm{r}}

, (refractive index of red colour) is minimum for visible light.

View answer and explanation

Correct option: A

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

Option A (If both Assertion and Reason are true and the Reason is a correct explanation of the Assertion) is correct because the critical angle depends on the refractive index, which is minimum for red light, leading to a maximum critical angle.

288 Medium

288 of 443

Application +4 | -1

The time taken by sunlight to cross a

5 \mathrm{~mm}

thick glass plate

(\mu=3 / 2)

View answer and explanation

Correct option: A

0.25 \times 10^{-10} \mathrm{~s}

Option A (

0.25 \times 10^{-10} \mathrm{~s}

) is correct because it's calculated by finding the speed of light in the glass and then dividing the thickness by that speed.

289 Medium

289 of 443

Application +4 | -1

A thin double convex lens has radii of curvature each of magnitude

\mathrm{40}\,\,\mathrm{cm}

and is made of glass with

\mu = 1.65

. The focal length of the lens in nearly

View answer and explanation

Correct option: B

\mathrm{31}\,\,\mathrm{cm}

Option B (

\mathrm{31}\,\mathrm{cm}

) is correct because the focal length is calculated using the lens maker's formula with the given refractive index and radii of curvature.

290 Medium

290 of 443

Analyzing +4 | -1

Assertion: A concave mirror and convex lens both have the same focal length in air. When they are submerged in water, they will have same focal length.

Reason: The refractive index of water is smaller than the refractive index of air.

View answer and explanation

Correct option: D

If the assertion and reason both are false.

Option D (If the assertion and reason both are false) is correct because the focal length of a mirror doesn't change in water, but the focal length of a lens does change, and the refractive index of water is greater than air.

291 Medium

291 of 443

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 gives the maximum base angle for total internal reflection at the hypotenuse, derived from Snell's law and the critical angle condition.

292 Medium

292 of 443

Remembering +4 | -1

Colour of the sky is blue due to

View answer and explanation

Correct option: A

Scattering of light

Option A (Scattering of light) is correct because the blue color of the sky is due to Rayleigh scattering, where shorter wavelengths are scattered more.

293 Medium

293 of 443

Application +4 | -1

A glass slab has the left half of refractive index

n_1

, and the right half of

n_2=3 n_1

. The effective refractive index of the whole slab is

View answer and explanation

Correct option: C

\frac{3 {n}_1}{2}

Option C (

\frac{{3 {n}_1}}{{2}}

) is correct because the effective refractive index is calculated by considering the total time taken for light to travel through the slab.

294 Medium

294 of 443

Analyzing +4 | -1

A person

\mathrm{6}\,\,\mathrm{feet}

in length can see his full size erect image in a mirror

\mathrm{2}\,\,\mathrm{feet}

in length. This mirror has to be

View answer and explanation

Correct option: C

Necessarily convex

Option D is correct because a person can see their full-size erect image in a plane mirror that is half their height, not necessarily a convex mirror.

295 Medium

295 of 443

Application +4 | -1

Two convex lenses of focal lengths

\mathrm{0}.\mathrm{03}\,\,\mathrm{m}\,\,{\mkern 1mu} \mathrm{and}\,\,{\mkern 1mu} \mathrm{0}.\mathrm{05}\,\,\mathrm{m}

are used to make a telescope. The distance kept between the two in order to obtain an image at infinity is

View answer and explanation

Correct option: A

\mathrm{0}\mathrm{.35}\,\,\mathrm{cm}

Option A (0.35 m) is correct because the distance between the lenses in a telescope adjusted for infinity is the sum of their focal lengths.

296 Medium

296 of 443

Remembering +4 | -1

Lux is equal to

View answer and explanation

Correct option: A

1\,\,lumen/{m^2}

Option A (

1 \, lumen/{m^2}

) is correct because lux is defined as lumens per square meter.

297 Medium

297 of 443

Understanding +4 | -1

A magnifying glass is used as the object to be viewed can be brought closer to the eye than the normal near point. This results in

View answer and explanation

Correct option: A

the formation of virtual erect image and larger angle to be subtended by the object at the eye and hence viewed in greater detail

Option A (the formation of virtual erect image and larger angle to be subtended by the object at the eye and hence viewed in greater detail) is correct because a magnifying glass allows the object to be closer, forming a virtual, erect, and magnified image.

298 Medium

298 of 443

Application +4 | -1

A person is in a room whose ceiling and two adjacent walls are mirrors. How many images are formed

View answer and explanation

Correct option: C

Option C (7) is correct because the two adjacent walls act as mirrors at 90 degrees, creating 3 images, and the ceiling mirror creates 4 additional images (including the person).

299 Medium

299 of 443

Understanding +4 | -1

Relative difference of focal lengths of objective and eye lens in the microscope and telescope is given as

View answer and explanation

Correct option: B

It is more in telescope

Option B (It is more in telescope) is correct because the focal length of the objective lens is much greater than the focal length of the eye lens in a telescope compared to a microscope.

300 Medium

300 of 443

Application +4 | -1

A thin biconvex lens of focal length

20 \mathrm{~cm}

is made of glass of refractive index 1.5. When it is dipped in a liquid of refractive index

\frac{9}{8}

, it acts as

View answer and explanation

Correct option: A

Convex lens of focal length 30 cm

Option A (Convex lens of focal length 30 cm) is correct because the focal length changes when the lens is immersed in a liquid, and the new focal length is calculated using the lens maker's formula.

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