CBSE Class 10 Science HOTs Reflection and Refraction Set 05

Reflection of Light

Question. The laws of reflection hold true for
(a) plane mirrors only
(b) concave mirrors only
(c) convex mirrors only
(d) all reflecting surface
Answer: (d) all reflecting surface

Question. What is the magnification of the images formed by plane mirrors and why?
Answer: The magnification of images formed by a plane mirror is +1. This is because the size of the image is exactly equal to the size of the object, and the image is virtual and erect, hence the positive sign.

Spherical Mirrors

Question. An optical device forms an erect image of an object placed in front of it. If the size of the image is one half that of the object, the optical device is a
(a) concave mirror
(b) convex mirror
(c) plane mirror
(d) convex lens.
Answer: (b) convex mirror

Question. The image of an object placed in front of a concave mirror of focal length 15 cm is of the same size as the object. The distance between the object and its image is
(a) 15 cm
(b) 30 cm
(c) 60 cm
(d) zero.
Answer: (d) zero.

Question. The relation \( R = 2f \) is valid
(a) for concave mirrors but not for convex mirrors
(b) for convex mirrors but not for concave mirrors
(c) neither for concave mirrors nor for convex mirrors
(d) for both concave and convex mirrors.
Answer: (d) for both concave and convex mirrors.

Question. The radius of curvature of a converging mirror is 30 cm. At what distance from the mirror should an object be placed so as to obtain a virtual image?
(a) Infinity
(b) 30 cm
(c) Between 15 cm and 30 cm
(d) Between 0 cm and 15 cm
Answer: (d) Between 0 cm and 15 cm

Question. An object of height 4 cm is kept at a distance of 30 cm from the pole of a diverging mirror. If the focal length of the mirror is 10 cm, the height of the image formed is
(a) +3.0 cm
(b) +2.5 cm
(c) +1.0 cm
(d) +0.75 cm
Answer: (c) +1.0 cm

Question. When an object is kept within the focus of a concave mirror, an enlarged image is formed behind the mirror. This image is
(a) real
(b) inverted
(c) virtual and inverted
(d) virtual and erect
Answer: (d) virtual and erect

Question. Define pole of a spherical mirror.
Answer: The center of the reflecting surface of a spherical mirror is a point called the pole. It usually lies on the surface of the mirror and is represented by the letter P.

Question. An object is placed at a distance of 30 cm in front of a convex mirror of focal length 15 cm. Write four characteristics of the image formed by the mirror.
Answer: The characteristics of the image are: (i) Virtual, (ii) Erect, (iii) Diminished, and (iv) Formed behind the mirror between the pole and the focus.

Question. List four specific characteristics of the images of the objects formed by convex mirrors.
Answer: Four characteristics of images formed by convex mirrors are: (i) Always virtual, (ii) Always erect, (iii) Always diminished in size, and (iv) Formed behind the mirror between the pole and the principal focus.

Question. An object is placed at a distance of 12 cm in front of a concave mirror of radius of curvature 30 cm. List four characteristics of the image formed by the mirror.
Answer: Here, \( R = 30 \text{ cm} \implies f = 15 \text{ cm} \). Since the object is placed at \( u = 12 \text{ cm} \), it is between the pole and focus (\( u < f \)). The characteristics are: (i) Virtual, (ii) Erect, (iii) Magnified (enlarged), and (iv) Formed behind the mirror.

Question. Name the type of mirrors used in the design of solar furnaces. Explain how high temperature is achieved by this device.
Answer: Concave mirrors are used in solar furnaces. High temperature is achieved because concave mirrors converge the parallel rays of sun falling on them to a single point called the principal focus. This concentration of solar energy at the focus produces intense heat.

Question. “The magnification produced by a spherical mirror is –3”. List four informations you obtain from this statement about the mirror/image.
Answer: The informations are: (i) The mirror is a concave mirror. (ii) The image is real. (iii) The image is inverted. (iv) The image is magnified three times the size of the object.

Question. List two possible ways in which a concave mirror can produce a magnified image of an object placed in front of it. State the difference if any between these two images.
Answer: A concave mirror produces a magnified image when: (i) The object is placed between C and F (produces a real and inverted magnified image). (ii) The object is placed between P and F (produces a virtual and erect magnified image). The main difference is that one image is real and inverted, while the other is virtual and erect.

Question. The magnification produced when an object is placed at a distance of 20 cm from a spherical mirror is +1/2. Where should the object be placed to reduce the magnification to +1/3?
Answer: Given \( u_1 = -20 \text{ cm} \) and \( m_1 = +1/2 \).
Since \( m = -v/u \implies 1/2 = -v_1 / (-20) \implies v_1 = 10 \text{ cm} \).
Using mirror formula: \( 1/f = 1/v_1 + 1/u_1 = 1/10 - 1/20 = 1/20 \)

\( \implies f = 20 \text{ cm} \) (Convex mirror).
Now, for \( m_2 = +1/3 \):
\( 1/3 = -v_2 / u_2 \implies v_2 = -u_2 / 3 \).
Substituting in mirror formula:
\( 1/20 = 1/(-u_2/3) + 1/u_2 = -3/u_2 + 1/u_2 = -2/u_2 \)

\( \implies u_2 = -40 \text{ cm} \).
So, the object should be placed at a distance of 40 cm from the mirror.

Question. A student has focused the image of an object of height 3 cm on a white screen using a concave mirror of focal length 12 cm. If the distance of the object from the mirror is 18 cm, find the values of the following:
(i) distance of the image from the mirror.
(ii) height of the image.
Answer: Given: \( h_o = 3 \text{ cm} \), \( f = -12 \text{ cm} \), \( u = -18 \text{ cm} \).
(i) Using mirror formula: \( 1/v = 1/f - 1/u = 1/(-12) - 1/(-18) = -3/36 + 2/36 = -1/36 \)

\( \implies v = -36 \text{ cm} \).
The image distance is 36 cm in front of the mirror.
(ii) Magnification \( m = -v/u = -(-36)/(-18) = -2 \).
Height of image \( h_i = m \times h_o = -2 \times 3 = -6 \text{ cm} \).
The height of the image is 6 cm (negative sign indicates it is inverted).

Question. Where should an object be placed in front of a concave mirror of focal length 20 cm so as to obtain a two times magnified virtual image of the object ?
Answer: For a virtual image in a concave mirror, magnification \( m = +2 \). Given \( f = -20 \text{ cm} \).
\( m = -\frac{v}{u} \)
\( \implies \) \( 2 = -\frac{v}{u} \)
\( \implies \) \( v = -2u \)
Using mirror formula: \( \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \)
\( \implies \) \( \frac{1}{-2u} + \frac{1}{u} = \frac{1}{-20} \)
\( \implies \) \( \frac{1}{2u} = -\frac{1}{20} \)
\( \implies \) \( 2u = -20 \)
\( \implies \) \( u = -10 \text{ cm} \).
The object should be placed at a distance of 10 cm in front of the mirror.

Question. A concave mirror has a focal length of 20 cm. At what distance from the mirror should a 4 cm tall object be placed so that it forms an image at a distance of 30 cm from the mirror? Also calculate the size of the image formed.
Answer: Given \( f = -20 \text{ cm} \), \( h_o = 4 \text{ cm} \), and for a real image formed by a concave mirror \( v = -30 \text{ cm} \).
Using mirror formula: \( \frac{1}{u} = \frac{1}{f} - \frac{1}{v} \)
\( \implies \) \( \frac{1}{u} = \frac{1}{-20} - \frac{1}{-30} \)
\( \implies \) \( \frac{1}{u} = -\frac{3}{60} + \frac{2}{60} = -\frac{1}{60} \)
\( \implies \) \( u = -60 \text{ cm} \).
Magnification \( m = -\frac{v}{u} = -\frac{-30}{-60} = -0.5 \).
Size of image \( h_i = m \times h_o = -0.5 \times 4 = -2 \text{ cm} \).
The size of the image is 2 cm and it is inverted.

Question. The image of a candle flame placed at a distance of 30 cm from a mirror is formed on a screen placed in front of the mirror at a distance of 60 cm from its pole. What is the nature of the mirror? Find its focal length. If the height of the flame is 2.4 cm, find the height of its image. State whether the image formed is erect or inverted.
Answer: Since the image is formed on a screen, it is a real image. Only a concave mirror forms a real image of an object. Thus, the nature of the mirror is concave.
Given \( u = -30 \text{ cm} \), \( v = -60 \text{ cm} \), \( h_o = 2.4 \text{ cm} \).
Mirror formula: \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} = \frac{1}{-60} + \frac{1}{-30} = -\frac{3}{60} \)
\( \implies \) \( f = -20 \text{ cm} \).
Magnification \( m = -\frac{v}{u} = -\frac{-60}{-30} = -2 \).
Height of image \( h_i = m \times h_o = -2 \times 2.4 = -4.8 \text{ cm} \).
The image is inverted.

Question. An object 4 cm in height is placed at 15 cm in front of a concave mirror of focal length 10cm. At what distance from the mirror should a screen be placed to obtain a sharp image of the object. Calculate the height of the image.
Answer: Given \( h_o = 4 \text{ cm} \), \( u = -15 \text{ cm} \), \( f = -10 \text{ cm} \).
\( \frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{-10} - \frac{1}{-15} = -\frac{3}{30} + \frac{2}{30} = -\frac{1}{30} \)
\( \implies \) \( v = -30 \text{ cm} \).
The screen should be placed 30 cm in front of the mirror.
\( m = -\frac{v}{u} = -\frac{-30}{-15} = -2 \).
\( h_i = m \times h_o = -2 \times 4 = -8 \text{ cm} \).
The height of the image is 8 cm.

Question. The image formed by a spherical mirror is real, inverted and its magnification is –2. If the image is at a distance of 30 cm from the mirror, where is the object placed? Find the focal length of the mirror. List two characteristics of the image formed if the object is moved 10 cm towards the mirror.
Answer: Given \( m = -2 \) and \( v = -30 \text{ cm} \).
\( m = -\frac{v}{u} \)
\( \implies \) \( -2 = -\frac{-30}{u} \)
\( \implies \) \( u = -15 \text{ cm} \).
Mirror formula: \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} = \frac{1}{-30} + \frac{1}{-15} = -\frac{3}{30} \)
\( \implies \) \( f = -10 \text{ cm} \).
If object moves 10 cm towards the mirror, new \( u = -15 + 10 = -5 \text{ cm} \).
Since \( u < f \), the image formed will be virtual, erect and magnified.

Question. (a) A security mirror used in a big showroom has radius of curvature 5 m. If a customer is standing at a distance of 20 m from the cash counter, find the position, nature and size of the image formed in the security mirror.
(b) Neha visited a dentist in his clinic. She observed that the dentist was holding an instrument fitted with a mirror. State the nature of this mirror and reason for its use in the instrument used by dentist.
Answer: (a) Given \( R = +5 \text{ m} \implies f = +2.5 \text{ m} \). \( u = -20 \text{ m} \).
\( \frac{1}{v} = \frac{1}{2.5} + \frac{1}{20} = 0.4 + 0.05 = 0.45 \)
\( \implies \) \( v = 2.22 \text{ m} \). Virtual, erect and diminished. (b) Nature: Concave mirror. It gives a magnified erect image of teeth when the tooth is held within its focus.

Question. If a lens and a spherical mirror both have a focal length of –15 cm, then it may be concluded that
(a) both are concave
(b) the lens is concave and the mirror is convex
(c) the lens is convex and the mirror is concave
(d) both are convex.
Answer: (a) both are concave

Question. A student determines the focal length of a device’ A’ by focussing the image of a far off object on a screen placed on the opposite side of the object. The device ‘A’ is
(a) concave lens
(b) concave mirror
(c) convex lens
(d) convex mirror.
Answer: (c) convex lens

Question. When light is incident on a glass slab, the incident ray, refracted ray and the emergent ray are in three media, A, B and C. If \( n_1, n_2 \) and \( n_3 \) are the refractive indices of A, B and C respectively and the emergent ray is parallel to the incident ray, which of the following is true?
(a) \( n_1 < n_2 < n_3 \)
(b) \( n_1 > n_2 > n_3 \)
(c) \( n_1 < n_2 = n_3 \)
(d) \( n_1 = n_3 < n_2 \)
Answer: (d) \( n_1 = n_3 < n_2 \)

Question. The image of a candle flame formed by a lens is obtained on a screen placed on the other side of the lens. According to new cartesian sign convention, if the image is three times the size of the flame, then the lens is
(a) concave and magnification is +3
(b) concave and magnification is –3
(c) convex and magnification is –3
(d) convex and magnification is +3.
Answer: (c) convex and magnification is –3

Question. The power of a combination of two lenses in contact is +1.0 D. If the focal length of one of the lenses of the combination is +20.0 cm, the focal length of the other lens would be
(a) –120.0 cm
(b) +80.0 cm
(c) –25.0 cm
(d) –20.0 cm
Answer: (c) –25.0 cm

Question. An object of height 3.0 cm is placed vertically on the principal axis of a convex lens. When the object distance is –37.5 cm, an image of height –2.0 cm is formed at a distance of 25.0 cm from the lens. Next, the same object is placed vertically at 25.0 cm from the lens. In this situation the image distance v and height h of the image is (according to the new Cartesian sign convention)
(a) v = +37.5 cm; h = +4.5 cm
(b) v = –37.5 cm; h = +4.5 cm
(c) v = +37.5 cm; h = –4.5 cm
(d) v = –37.5 cm; h = –4.5 cm
Answer: (c) v = +37.5 cm; h = –4.5 cm

Question. A lens has a power of +4.0 D. It is
(a) a convex lens of focal length 4 m
(b) a concave lens of focal length 4 m
(c) a convex lens of focal length 0.25 m
(d) a concave lens of focal length 0.25 m.
Answer: (c) a convex lens of focal length 0.25 m

Question. An object is placed in front of a concave lens. For all positions of the object the image formed is always
(a) real, diminished and inverted
(b) virtual, diminished and erect
(c) real, enlarged and erect
(d) virtual, erect and enlarged.
Answer: (b) virtual, diminished and erect

Question. A ray of light starting from air passes through medium A of refractive index 1.50, enters medium B of refractive index 1.33 and finally enters medium C of refractive index 2.42. If this ray emerges out in air from C, then for which of the following pairs of media the bending of light is least?
(a) air-A
(b) A-B
(c) B-C
(d) C-air
Answer: (b) A-B

Question. The refractive index of medium A is 1.5 and that of medium B is 1.33. If the speed of light in air is \( 3 \times 10^8 \) m/s, what is the speed of light in medium A and B respectively?
(a) \( 2 \times 10^8 \) m/s and \( 1.33 \times 10^8 \) m/s
(b) \( 1.33 \times 10^8 \) m/s and \( 2 \times 10^8 \) m/s
(c) \( 2.25 \times 10^8 \) m/s and \( 2 \times 10^8 \) m/s
(d) \( 2 \times 10^8 \) m/s and \( 2.25 \times 10^8 \) m/s
Answer: (d) \( 2 \times 10^8 \) m/s and \( 2.25 \times 10^8 \) m/s

Question. If a lens can converge the sun rays at a point 20 cm away from its optical centre, the power of this lens is
(a) +2D
(b) –2D
(c) +5D
(d) –5D
Answer: (c) +5D

Question. A converging lens forms a three times magnified image of an object, which can be taken on a screen. If the focal length of the lens is 30 cm, then the distance of the object from the lens is
(a) –55 cm
(b) –50 cm
(c) –45 cm
(d) –40 cm
Answer: (d) –40 cm

Question. Assertion (A) : A concave lens of very short focal length causes higher divergence than one with longer focal length.
Reason (R) : The power of a lens is directly proportional to its focal length.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
Answer: (c) Assertion (A) is true, but Reason (R) is false.

Question. Assertion (A) :The SI unit of power of lens is ‘dioptre’.
Reason (R) : The power of a concave lens is positive and that of a convex lens is negative.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
Answer: (c) Assertion (A) is true, but Reason (R) is false.

Question. The refractive index of glass is 1.50. What is the meaning of this statement?
Answer: It means that the speed of light in air or vacuum is 1.50 times the speed of light in glass. Alternatively, the speed of light in glass is \( \frac{1}{1.50} \) times the speed of light in vacuum.

Question. What is meant by power of a lens?
Answer: Power of a lens is defined as the degree of convergence or divergence of light rays achieved by it. It is mathematically expressed as the reciprocal of the focal length of the lens in meters.