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YOUR STUDY SPACE · CBSE

Light – Reflection and Refraction — Class 10 Science

Science · Chapter 9

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Chapter summary

Light travels in straight lines and changes direction when it meets surfaces or different media. Reflection follows two laws — the angle of incidence equals the angle of reflection, and the incident ray, reflected ray and normal lie in one plane. Spherical mirrors (concave and convex) form images whose nature, position and size are found using ray diagrams and the mirror formula 1/v + 1/u = 1/f, with magnification m = −v/u. Refraction is the bending of light as it passes from one medium to another, governed by Snell’s law and described by the refractive index. Lenses (convex and concave) form images using the lens formula 1/v − 1/u = 1/f, and the power of a lens is measured in dioptres. These ideas explain everyday optics from mirrors and magnifiers to cameras.
Reflection and spherical mirrorsMirror formula and magnificationRefraction and refractive indexLenses and the lens formulaPower of a lens

Key ideas & terms

Laws of reflection
Angle of incidence equals angle of reflection; rays and normal are coplanar.
Refractive index
A measure of how much a medium bends light.
Mirror/lens formula
Relation linking object distance, image distance and focal length.
Power of a lens
The reciprocal of focal length (in metres), measured in dioptres.

Extra questions & answers

Why does a ray of light bend when it enters water from air?

Light slows down in the denser medium, so it bends towards the normal — this is refraction.

What kind of mirror is used as a rear-view mirror in vehicles, and why?

A convex mirror, because it gives an erect, diminished image and a wider field of view.

State the laws of reflection of light.

The angle of incidence equals the angle of reflection, and the incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane.

Where should an object be placed before a concave mirror to get a magnified, virtual image?

Between the pole and the focus; the image formed is virtual, erect and larger than the object (refer to the ray diagram in your NCERT textbook).

Why is a convex mirror used as a rear-view mirror in vehicles?

Because it always forms an erect, diminished image and gives a wider field of view of the traffic behind.

Write the mirror formula and the magnification formula.

The mirror formula is , and the magnification is .

What is refraction of light, and why does it occur?

The bending of light as it passes from one transparent medium to another; it occurs because the speed of light changes in different media.

What is the refractive index of a medium?

A measure of how much a medium slows down and bends light, given by the ratio of the speed of light in vacuum to its speed in the medium.

Write the lens formula and explain the power of a lens.

The lens formula is ; the power of a lens is the reciprocal of its focal length in metres , measured in dioptres (D).

How does a convex lens form a real, inverted image, and where is it used?

When the object is beyond the focus, a convex lens forms a real, inverted image on the other side; such lenses are used in cameras, projectors and the human eye (refer to the ray diagram in your NCERT textbook).

QUESTIONS

1. Define the principal focus of a concave mirror.

The principal focus of a concave mirror is the point on its principal axis at which rays parallel to the principal axis meet after reflection from the mirror.

2. The radius of curvature of a spherical mirror is . What is its focal length?

For a spherical mirror, . Therefore, Its focal length is .

3. Name a mirror that can give an erect and enlarged image of an object.

A concave mirror can give an erect and enlarged image when the object is placed between its pole and principal focus.

4. Why do we prefer a convex mirror as a rear-view mirror in vehicles?

A convex mirror is preferred as a rear-view mirror because it always forms an erect and diminished image and provides a wider field of view. It therefore enables the driver to see a larger area of the traffic behind the vehicle.

QUESTIONS

1. Find the focal length of a convex mirror whose radius of curvature is .

For a spherical mirror, . Hence, Since the mirror is convex, its focal length is positive according to the New Cartesian Sign Convention. Thus, .

2. A concave mirror produces three times magnified (enlarged) real image of an object placed at in front of it. Where is the image located?

For a real, inverted image, the magnification is negative. Therefore, , and the object distance is . Using we get and hence The image is located in front of the mirror.

QUESTIONS

1. A ray of light travelling in air enters obliquely into water. Does the light ray bend towards the normal or away from the normal? Why?

The light ray bends towards the normal because it travels from air, which is optically rarer, into water, which is optically denser. Its speed decreases on entering water.

2. Light enters from air to glass having refractive index . What is the speed of light in the glass? The speed of light in vacuum is .

The refractive index is given by Therefore, The speed of light in the glass is .

3. Find out, from Table 9.3, the medium having highest optical density. Also find the medium with lowest optical density.

Diamond has the highest optical density because it has the highest refractive index, . Air has the lowest optical density because it has the lowest refractive index, .

4. You are given kerosene, turpentine and water. In which of these does the light travel fastest? Use the information given in Table 9.3.

Light travels fastest in the medium with the lowest refractive index. The refractive indices of water, kerosene and turpentine oil are , and , respectively. Therefore, light travels fastest in water.

5. The refractive index of diamond is . What is the meaning of this statement?

It means that the ratio of the speed of light in air or vacuum to its speed in diamond is . Thus, In other words, light travels times faster in vacuum than in diamond.

QUESTIONS

1. Define dioptre of power of a lens.

One dioptre is the power of a lens whose focal length is . Thus,

2. A convex lens forms a real and inverted image of a needle at a distance of from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.

A convex lens forms a real image equal in size to the object when the object is placed at twice the focal length. Since the image is formed at , the needle is also placed in front of the lens. Thus, and The power is Therefore, the needle is placed in front of the lens and its power is .

3. Find the power of a concave lens of focal length .

The focal length of a concave lens is negative, so . Therefore, The power of the lens is .

EXERCISES

1. Which one of the following materials cannot be used to make a lens?
(a) Water (b) Glass (c) Plastic (d) Clay

(d) Clay. A lens must be made of a transparent material so that light can pass through and be refracted. Clay is opaque.

2. The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should be the position of the object?
(a) Between the principal focus and the centre of curvature
(b) At the centre of curvature
(c) Beyond the centre of curvature
(d) Between the pole of the mirror and its principal focus.

(d) Between the pole of the mirror and its principal focus. In this position, a concave mirror forms a virtual, erect and enlarged image behind the mirror.

3. Where should an object be placed in front of a convex lens to get a real image of the size of the object?
(a) At the principal focus of the lens
(b) At twice the focal length
(c) At infinity
(d) Between the optical centre of the lens and its principal focus.

(b) At twice the focal length. An object placed at forms a real, inverted image of equal size at .

4. A spherical mirror and a thin spherical lens have each a focal length of . The mirror and the lens are likely to be
(a) both concave.
(b) both convex.
(c) the mirror is concave and the lens is convex.
(d) the mirror is convex, but the lens is concave.

(a) Both concave. Under the New Cartesian Sign Convention, a concave mirror and a concave lens both have negative focal lengths.

5. No matter how far you stand from a mirror, your image appears erect. The mirror is likely to be
(a) only plane.
(b) only concave.
(c) only convex.
(d) either plane or convex.

(d) Either plane or convex. A plane mirror always forms an erect image, and a convex mirror also always forms an erect image for every object position.

6. Which of the following lenses would you prefer to use while reading small letters found in a dictionary?
(a) A convex lens of focal length .
(b) A concave lens of focal length .
(c) A convex lens of focal length .
(d) A concave lens of focal length .

(c) A convex lens of focal length . A convex lens acts as a magnifying glass when the letters are within its focal length. A shorter focal length gives greater magnification.

7. We wish to obtain an erect image of an object, using a concave mirror of focal length . What should be the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or smaller than the object? Draw a ray diagram to show the image formation in this case.

The object must be placed between the pole and the principal focus of the concave mirror. Therefore, its distance from the mirror must be less than , or . The image formed is virtual, erect and larger than the object, and it appears behind the mirror. For the ray diagram, draw one ray from the top of the object parallel to the principal axis; after reflection it passes through the principal focus. Draw another ray towards the pole and reflect it according to the laws of reflection. Extend the reflected rays backward behind the mirror. Their extensions meet at the enlarged, erect virtual image.

8. Name the type of mirror used in the following situations.
(a) Headlights of a car.
(b) Side/rear-view mirror of a vehicle.
(c) Solar furnace.
Support your answer with reason.

(a) A concave mirror is used in car headlights. When the bulb is placed at its principal focus, the reflected light forms a strong parallel beam.
(b) A convex mirror is used as a side or rear-view mirror because it forms an erect, diminished image and provides a wide field of view.
(c) A concave mirror is used in a solar furnace because it converges sunlight at its principal focus, producing a high temperature.

9. One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answer experimentally. Explain your observations.

Yes, the lens will still produce a complete image, but the image will be less bright. Every small portion of a convex lens receives rays from all parts of the object and can form the whole image. To verify this, form a sharp image of a bright object on a screen using a convex lens. Cover half of the lens with black paper without changing the positions of the object, lens or screen. The complete image remains visible, but its brightness decreases because fewer light rays pass through the lens.

10. An object in length is held away from a converging lens of focal length . Draw the ray diagram and find the position, size and the nature of the image formed.

Here, , and . Using the lens formula, Therefore, The magnification is Hence, The image is formed about on the opposite side of the lens. It is real, inverted and diminished, with a size of about . In the ray diagram, the object lies beyond , and the image lies between and .

11. A concave lens of focal length forms an image from the lens. How far is the object placed from the lens? Draw the ray diagram.

For a concave lens, , and its virtual image has . Using Therefore, and The object is placed in front of the lens. In the ray diagram, draw one incident ray parallel to the principal axis; after refraction it appears to diverge from the principal focus on the object's side. A second ray through the optical centre passes undeviated. Their backward extensions meet between the optical centre and the focus, forming a virtual, erect and diminished image.

12. An object is placed at a distance of from a convex mirror of focal length . Find the position and nature of the image.

Here, and . Using the mirror formula, Thus, so The image is formed behind the mirror. It is virtual, erect and diminished.

13. The magnification produced by a plane mirror is . What does this mean?

A magnification of means that the image is erect because the magnification is positive, and its size is equal to the size of the object because the magnitude of magnification is . The image formed by the plane mirror is virtual and laterally inverted.

14. An object in length is placed at a distance of in front of a convex mirror of radius of curvature . Find the position of the image, its nature and size.

For the convex mirror, Also, and . Using the mirror formula, Therefore, so The image is formed about behind the mirror. Its magnification is Thus, The positive image height shows that the image is erect. It is virtual, erect and diminished, with a size of approximately .

15. An object of size is placed at in front of a concave mirror of focal length . At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and the nature of the image.

Here, , and . Using the mirror formula, Therefore, so The screen should be placed in front of the mirror. The magnification is Hence, The image is real, inverted and enlarged, and its size is .

16. Find the focal length of a lens of power . What type of lens is this?

Using the focal length is The negative focal length shows that it is a concave or diverging lens.

17. A doctor has prescribed a corrective lens of power . Find the focal length of the lens. Is the prescribed lens diverging or converging?

Using Thus, the focal length is approximately , or . Since its focal length and power are positive, the prescribed lens is a convex or converging lens.