JEE Advanced PYQ Physics – Plane Mirror, Spherical Mirror & Reflection of Light

Q 1 :

A ray of light travelling in the direction $\frac{1}{2} (\hat{i} + \sqrt{3} \hat{j})$ is incident on a plane mirror. After reflection, it travels along the direction $\frac{1}{2} (\hat{i} - \sqrt{3} \hat{j}) .$ The angle of incidence is [2013]

$30 °$
$45 °$
$60 °$
$75 °$

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(1)

[IMAGE 1016]

From figure,

$\tan i = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}}$

$∴$ $i = 30 °$

(Angle of incidence)

Q 2 :

In an experiment to determine the focal length $(f)$ of a concave mirror by the $u - v$ method, a student places the object pin A on the principal axis at a distance $x$ from the pole P. The student looks at the pin and its inverted image from a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then, [2007]

$x < f$
$f < x < 2 f$
$x = 2 f$
$x > 2 f$

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(2)

As shown in the figure, when the object (O) is placed between F and C, the image $(I)$ is formed beyond C. It is in this condition that when the student shifts his eyes towards the left, the image appears to the right of the object pin. Object O lies between focus $(f)$ and centre of curvature $(2 f)$ $f < x < 2 f .$

[IMAGE 1017]

Q 3 :

A point source of light B is placed at a distance L in front of the centre of a mirror of width $' d'$ hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown in the figure. The greatest distance over which he can see the image of the light source in the mirror is [2000]

[IMAGE 1018]

$\frac{d}{2}$
$d$
$2 d$
$3 d$

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(4)

[IMAGE 1019]

The ray diagram is as follows:

From figure, $W X = P Q = d$

$Z S = R S = \frac{d}{2}$

$∵$ $P W = 2 P S$

$∴$ $V W = 2 R S = 2 (\frac{d}{2}) = d$

Similarly, $X Y = d$

$∴$ $V Y = V W + W X + X Y = d + d + d = 3 d$

Q 4 :

A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight path on the flat ground. The lamp post and the person are always perpendicular to the ground. If the speed of the person is 60 cm $s^{- 1}$ , the speed of the tip of the person's shadow on the ground with respect to the person is _____ cm $s^{- 1}$ . [2023]

(40)

[IMAGE 1020]

$From figure, ∆ A B E and ∆ C D E are similar triangles, so$

$\frac{4}{y} = \frac{1.6}{y - x}$ $\Rightarrow 4 (y - x) = 1.6 y$

$\Rightarrow 4 y - 4 x = 1.6 y$

$\Rightarrow 2.4 y = 4 x$

$∴$ $x = 0.6 y$

Differentiating both sides,

$\frac{d x}{d t} = 0.6 \frac{d y}{d t}$

$(\frac{d x}{d t} = speed of person = 60 cm/s and \frac{d y}{d t} = speed of tip of person's shadow)$

$60 = 0.6 \frac{d y}{d t}$ $∴$ $\frac{d y}{d t} = 100 cm/s$

Speed of tip of person's shadow on the ground, w.r.t. person $= 100 - 60 = 40 cm/s$

Q 5 :

An object and a concave mirror of focal length $f = 10 cm$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_{0} = 15 cm s^{- 1}$ towards the mirror with respect to the laboratory frame. The distance between the object and the mirror at a given moment is denoted by $u$ . When $u = 30 cm$ , the speed of the mirror $V_{m}$ is such that the image is instantaneous at rest with respect to the laboratory frame, and the object forms a real image. The magnitude of $V_{m}$ is _____ $cm s^{- 1}$ . [2022]

[IMAGE 1021]

(3)

$We have, u = - 30 cm, f = - 10 cm$

$\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{- 10} - \frac{1}{- 30} = \frac{1}{30} - \frac{1}{10} = \frac{1 - 3}{30} = - \frac{1}{15}$

So, $v = - 15 cm$

[IMAGE 1022]

As, ${\vec{V}}_{I, M} = - {(\frac{v}{u})}^{2} {\vec{V}}_{O, M}$

$\Rightarrow {\vec{V}}_{I} - {\vec{V}}_{M} = - {(\frac{v}{u})}^{2} ({\vec{V}}_{O} - {\vec{V}}_{M})$

$\Rightarrow 0 - {\vec{V}}_{M} = - \frac{1}{4} (15 \hat{i} - {\vec{V}}_{M})$

$\Rightarrow - {\vec{V}}_{M} = - \frac{15}{4} \hat{i} + \frac{1}{4} {\vec{V}}_{M}$

$\Rightarrow - \frac{5}{4} {\vec{V}}_{M} = - \frac{15}{4} \hat{i}$

$∴$ ${\vec{V}}_{M} = 3 \hat{i}$

Q 6 :

Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $\frac{25}{3} m$ to $\frac{50}{7} m$ in 30 seconds. What is the speed of the object in km per hour ? [2010]

(3)

$Using mirror formula for first position$

$u_{1} = ?, v_{1} = \frac{25}{3} cm, f = + 10 cm (= \frac{R}{2})$

$\frac{1}{v_{1}} + \frac{1}{u_{1}} = \frac{1}{f}, \frac{3}{25} + \frac{1}{u_{1}} = \frac{1}{10}$ $∴$ $u_{1} = - 50 cm$

$Using mirror formula for the second position$

$u_{2} = ?, v_{2} = \frac{50}{7} cm, f = 10 cm$

$\frac{1}{v_{2}} + \frac{1}{u_{2}} = \frac{1}{f}$ $\Rightarrow \frac{7}{50} + \frac{1}{u_{2}} = \frac{1}{10}$ $\Rightarrow \frac{1}{u_{2}} = \frac{1}{10} - \frac{7}{50}$

$∴$ $u_{2} = - 25 cm$

$Speed of object = \frac{u_{1} - u_{2}}{time} = \frac{25}{30} \times \frac{18}{5} = 3 {km h}^{- 1}$

Q 7 :

Three plane mirrors form an equilateral triangle with each side of length L. There is a small hole at a distance $l > 0$ from one of the corners as shown in the figure. A ray of light is passed through the hole at an angle $θ$ and can only come out through the same hole. The cross section of the mirror configuration and the ray of light lie on the same plane. [2022]

[IMAGE 1023]

Which of the following statement(s) is(are) correct?

The ray of light will come out for $θ = 30 °$ , for $0 < l < L$ .
There is an angle for $l = \frac{L}{2}$ at which the ray of light will come out after two reflections.
The ray of light will NEVER come out for $θ = 60 °$ , and $l = \frac{L}{3} .$
The ray of light will come out for $θ = 60 °$ , and $0 < l < \frac{L}{2}$ after six reflections.

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Select one or more options

(1, 2)

As we can see, for $θ = 30 °$ the ray will be incident normally and hence will retrace its path $\Rightarrow$ (1) is correct.

[Image 1024]

For $θ = 60 °, ℓ = \frac{L}{2},$ then, we get the ray diagram shown below. Clearly, the ray of light comes out after two reflections $\Rightarrow$ (2) is correct.

[IMAGE 1025]

If $θ = 60 °$ and $ℓ = \frac{L}{3},$ then we get the ray diagram as shown below.

[IMAGE 1026]

Clearly, after 5 reflections, the ray comes out. So (3) and (4) are incorrect.

Q 8 :

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length, $f$ , as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.) [2018]

[IMAGE 1027]

[IMAGE 1028]
[IMAGE 1029]
[IMAGE 1030]
[IMAGE 1031]

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(4)

$Distance of point A from the mirror is \frac{f}{2} .$

[IMAGE 1032]

From mirror formula,

$\frac{1}{v} + \frac{1}{f / 2} = \frac{1}{- f}$ $\Rightarrow \frac{1}{v} = \frac{2}{f} - \frac{1}{f} = \frac{1}{f}$ $∴$ $v = f$

Image $A' B'$ of line AB should be $I$ principal axis. Image of $F$ will be formed at infinity.

As light rays from infinity or towards infinity seem parallel to the principal axis of the mirror.

Q 9 :

A student performed the experiment of determination of focal length of a concave mirror by $u - v$ method using an optical bench of length 1.5 meter. The focal length of the mirror used is 24 cm. The maximum error in the location of the image can be 0.2 cm. The 5 sets of $(u, v)$ values recorded by the student (in cm) are:

(42, 56), (48, 48), (60, 40), (66, 33), (78, 39).

The data set(s) that cannot come from experiment and is (are) incorrectly recorded, is (are) [2009]

(42, 56)
(48, 48)
(66, 33)
(78, 39)

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Select one or more options

(3, 4)

$Given f = - 24 cm$

Applying mirror formula, $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

The $u - v$ values of options (1) and (2) match with mirror formula, whereas options (3) and (4) do not match with mirror formula.

For $(66, 33)$ ,

$\Rightarrow \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{- 24} + \frac{1}{66} = \frac{- 66 + 24}{24 \times 66} = \frac{- 42}{24 \times 66}$

$\Rightarrow v = - \frac{24 \times 66}{42} = - 37.7 cm$

But the value of $v = 33 cm$ . The absolute error is $37.7 - 33 = 4.7 cm,$ which is greater than $0.2 cm$ . Therefore, it is a wrong reading. For $(78, 39)$ , when $u = 78$ , then

$\frac{1}{v} + \frac{1}{- 78} = \frac{1}{- 24}$ $\Rightarrow v = - 34.67 cm$

The absolute error is $39 - 34.67 = 4.33 cm,$ which is greater than $0.2 cm$ .

Q 10 :

STATEMENT-1: The formula connecting $u, v$ and $f$ for a spherical mirror is valid for mirrors whose sizes are very small compared to their radii of curvature.

STATEMENT-2: Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces. [2007]

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
Statement-1 is True, Statement-2 is False
Statement-1 is False, Statement-2 is True

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(3)

The formula connecting $u, v$ and $f$ for a spherical mirror $\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$ is valid only for mirrors of small apertures, where the size of the aperture is very small as compared to the radius of curvature of the mirror.

Laws of reflection are valid for plane as well as large spherical surfaces. The laws of reflection are valid whenever the light is reflected.

Topic Question Set

Q 1 :

A ray of light travelling in the direction $\frac{1}{2} (\hat{i} + \sqrt{3} \hat{j})$ is incident on a plane mirror. After reflection, it travels along the direction $\frac{1}{2} (\hat{i} - \sqrt{3} \hat{j}) .$ The angle of incidence is [2013]

Q 6 :

Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $\frac{25}{3} m$ to $\frac{50}{7} m$ in 30 seconds. What is the speed of the object in km per hour ? [2010]

Q 10 :

STATEMENT-1: The formula connecting $u, v$ and $f$ for a spherical mirror is valid for mirrors whose sizes are very small compared to their radii of curvature.

STATEMENT-2: Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces. [2007]

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Topic Question Set

Q 1 : A ray of light travelling in the direction 12(i^+3j^) is incident on a plane mirror. After reflection, it travels along the direction 12(i^-3j^). The angle of incidence is [2013]

Q 6 : Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from 253m to 507m in 30 seconds. What is the speed of the object in km per hour ? [2010]

Q 10 : STATEMENT-1: The formula connecting u,v and f for a spherical mirror is valid for mirrors whose sizes are very small compared to their radii of curvature. STATEMENT-2: Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces. [2007]

Want Us to Email you About Special Offers & Updates?

Q 1 :

A ray of light travelling in the direction $\frac{1}{2} (\hat{i} + \sqrt{3} \hat{j})$ is incident on a plane mirror. After reflection, it travels along the direction $\frac{1}{2} (\hat{i} - \sqrt{3} \hat{j}) .$ The angle of incidence is [2013]

Q 6 :

Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $\frac{25}{3} m$ to $\frac{50}{7} m$ in 30 seconds. What is the speed of the object in km per hour ? [2010]

Q 10 :

STATEMENT-1: The formula connecting $u, v$ and $f$ for a spherical mirror is valid for mirrors whose sizes are very small compared to their radii of curvature.

STATEMENT-2: Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces. [2007]