CBSE Class 10 Science HOTs Reflection and Refraction Set 04

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

Question. A convex lens forms a virtual image when an object is placed at a distance of \( 20 \text{ cm} \) from it. The focal length of the lens is
(a) \( f = 40 \text{ cm} \)
(b) \( f = 20 \text{ cm} \)
(c) \( f > 20 \text{ cm} \)
(d) \( f < 20 \text{ cm} \)
Answer: (c) \( f > 20 \text{ cm} \)

Question. The refractive index of water, sulphuric acid, glass and carbon disulphide are \( 1.33 \), \( 1.43 \), \( 1.53 \) and \( 1.63 \) respectively. The light travel slowest in
(a) glass
(b) water
(c) sulphuric acid
(d) carbon disulphide
Answer: (d) carbon disulphide

Question. When a ray passing through focus strikes concave lens, the refracted ray will
(a) retrace its path
(b) emerge parallel to the principal axis
(c) emerge perpendicular to the principal axis
(d) emerge through a focus on another side
Answer: (b) emerge parallel to the principal axis

Direction: In the following Questions, the Assertion and Reason have been put forward. Read the statements carefully and choose the correct alternative from the following:
(a) Both the Assertion and the Reason are correct and the Reason is the correct explanation of the Assertion.
(b) Both the Assertion and the Reason are correct but the Reason is not the correct explanation of the Assertion.
(c) Assertion is true but the Reason is false.
(d) The statement of the Assertion is false but the Reason is true.

Question. Assertion: A concave lens of very short focal length causes higher divergence than one with the longer focal length.
Reason: The power of lens is directly proportional to its focal length.
(a) A
(b) B
(c) C
(d) D
Answer: (c) Assertion is true but the Reason is false.

Question. Assertion: The centre of curvature lies outside the reflecting surface of spherical mirror and is not a part of mirror.
Reason: The reflecting surface of a spherical mirror forms a part of a sphere which has a centre.
(a) A
(b) B
(c) C
(d) D
Answer: (a) Both the Assertion and the Reason are correct and the Reason is the correct explanation of the Assertion.

Question. A ray of light enters into benzene from air. If the refractive index of benzene is \( 1.50 \), by what percent does the speed of light reduce on entering the benzene?
Answer: Refractive index \( n = \frac{c}{v} \) \( \implies \) \( 1.50 = \frac{c}{v} \) \( \implies \) \( v = \frac{c}{1.50} \). Percentage decrease in speed \( = \frac{c - v}{c} \times 100 = \frac{c - c/1.50}{c} \times 100 = \left( 1 - \frac{1}{1.50} \right) \times 100 = \frac{0.50}{1.50} \times 100 = \frac{1}{3} \times 100 = 33.33\% \).

Question. List four properties of the image formed by a concave mirror when an object is placed between the focus and pole of the mirror.
Answer: 1. The image is virtual.
2. The image is erect.
3. The image is magnified (larger than the object).
4. The image is formed behind the mirror.

Question. (a) Define unit of a power of a lens.
(b) A converging lens has a focal length of \( 250 \text{ mm} \). Calculate its power and express it according to Sign Convention.
Answer: (a) The SI unit of power of a lens is dioptre (D). One dioptre is the power of a lens whose focal length is \( 1 \text{ metre} \).
(b) Given \( f = +250 \text{ mm} = +0.25 \text{ m} \).
Power \( P = \frac{1}{f(\text{in m})} = \frac{1}{+0.25} = +4\text{D} \).

Question. The image of a candle flame placed at a distance of \( 36 \text{ cm} \) from a spherical lens is formed on a screen placed at a distance of \( 72 \text{ cm} \) from the lens. Identify the type of lens and calculate its focal length. If the height of the flame is \( 2.5 \text{ cm} \), find the height of the image.
Answer: Since the image is formed on a screen, it is a real image. Only a convex lens can form a real image. Thus, it is a convex lens.
Given: \( u = -36 \text{ cm} \), \( v = +72 \text{ cm} \), \( h_o = 2.5 \text{ cm} \).
Using lens formula: \( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{72} - \frac{1}{-36} = \frac{1+2}{72} = \frac{3}{72} = \frac{1}{24} \)

\( \implies \) \( f = +24 \text{ cm} \).
Magnification \( m = \frac{v}{u} = \frac{h_i}{h_o} \)

\( \implies \) \( \frac{72}{-36} = \frac{h_i}{2.5} \)

\( \implies \) \( -2 = \frac{h_i}{2.5} \)

\( \implies \) \( h_i = -5.0 \text{ cm} \). The height of the image is \( 5.0 \text{ cm} \) (inverted).

Question. (a) A student holding mirror in his hand, directed the reflecting surface of a mirror towards the Sun. He then directed the reflected light on to a sheet of paper held close to the mirror.
(i) What should he do to burn the paper?
(ii) What type of mirror does he have?
(iii) Will he be able to determine the appropriate value of focal lengh of this mirror from this activity? Give reason for your answer in this case.
Answer: (i) The student should adjust the distance between the mirror and the paper until a sharp, bright spot (the image of the sun) is formed on the paper and hold it there for some time.
(ii) He has a concave mirror.
(iii) Yes. The distance between the mirror and the bright spot on the paper is the approximate focal length of the mirror because light rays from a very distant object like the sun are parallel and converge at the principal focus after reflection.

Question. A student took three concave mirrors of different focal lengths and performed the experiment to see the image formation by placing an object at different distances with these mirrors as shown in the following table.

Now answer the following questions:
(a) List two properties of the image formed in case I.
(b) In which one of the cases given in the table, the mirror will form real image of same size and why?
(c) Name the type of mirror used by dentists. Give reason why do they use such type of mirrors.
Answer: (a) In Case I, \( u = 45 \text{ cm} \), \( f = 20 \text{ cm} \). Since \( u > 2f \), the image is real, inverted and diminished.
(b) In Case II, because \( u = 30 \text{ cm} \) and \( f = 15 \text{ cm} \), so \( u = 2f \). When an object is placed at the centre of curvature, a concave mirror forms a real image of the same size.
(c) Dentists use concave mirrors. When the object (tooth) is placed between the pole and the focus of the mirror, it produces a virtual, erect, and magnified image, allowing them to see details clearly.