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**Solved Examples**

**Ex.1: Where is the image of an object placed 7 centimeters away from a 5 centimeter focal length of a Convex lens? Concave mirror? Are the images real or virtual in each case?**

**Sol.:** A convex lens has a positive focal length. We can apply the lens equation: 1/f = 1/v – 1/u.

This gives: 1/5 = –1/7 + 1/v. Solving for v = 17.5 cm. The image is real since v is positive. A concave mirror also has a negative focal length so we get the same result (the image is real and 17.5 centimeters in front of the mirror).

**Ex. 2: A laserbeam strikes a vertical surface at an angle of 48°. The reflected beam can be seen as a spot on a horizontal surface. The spot is 10 meters away from the point of incidence on the vertical surface. How far is the horizontal distance from the spot to the vertical surface?**

**Sol.:** The angle of reflection is equal to the angle of incidence, so it is 48°. Thus the angle between the vertical surface and the reflected beam is 90 – 48 = 42°. The reflected beam is 10 meters long so its horizontal projection is given by 10 sin (42°) = 6.7 meters.

**Ex.3: A convex lens of focal length 25 cm and a concave lens of focal length 10 cm are placed in close ccontact with each other.**

**i) What is the power of this combination?**

**ii) What is the focal length of this combination?**

Thus, the focal length of this combination of lenses is –16.6 cm.

**Ex. 4: The speed of light in air is 3 × 10 ^{8} m/s and the speed of light in water is 2.26 × 10^{8} m/s. Find the refractive index of water.**

**Ex.5: A convex mirror used for rear-view on an automobile has a radius of curvature of 3.00 m. If a bus is located at 5.00 m from this mirror, find the position, nature and size of the image.**

**Sol.:** Radius of curvature, R = + 3.00 m

Object-distance, u = –5.00 m

Image-distance, v = ?

Height of the image h´ = ?

The image is virtual, erect and smaller in size by a factor of 0.23.

**Ex.6: A 2.0 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 10 cm. The distance of the object from the lens is 15 cm. Find the nature, position and size of the image. Also find its magnification.**

**Sol.:** Height of the object h = + 2.0 cm

Focal length f = + 10 cm

Object-distance u = – 15 cm

Image-distance v = ?

Height of the image h´ = ?

In the following videos we have explained you about the concept of Light and its properties. Watch this video to understand the concepts and also post your questions and comments in the comments section.

The negative signs of m and h´ show that the image is inverted and real. It is formed below the principal axis. Thus, a real, inverted image, 4 cm tall, is formed at a distance of 30 cm on the other side of the lens. The image is two times enlarged.

**Basic Level assignment**

1. An object is kept in front of a concave mirror of focal length 15 cm. The image formed is three times the size of the object. Calculate the two ossible distances of the object from the mirror.

2. A concave mirror is placed in water. Will there be any change in the focal length? Give reason.

3. Calculate the speed of light in a medium, whose critical angle is 45°.

4. A beaker is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the beaker is measured to be 9.4 cm. What is the refractive index of water?

5. Magnification m = + 1 for a plane mirror. What is the significance of m = 1 and the + sign of m?

6. An object is placed at 0.06 m from a convex lens of focal length 0.10 m. Calculate the position of the image.

7. Two thin lenses of focal lengths + 10 cm and – 5 cm. are kept in contact. What is the

(a) focal length (b) power of the combination?

8. If the power of lens is +5 dioptre, what is its focal length?

9. Two thin lenses of power +5 D and – 3 D are in contact. What is the focal length of the combination?

10. Where should an object be placed from a converging lens of focal length 20 cm, so as to obtain a real image of magnification 2?

**Light Class VIII-Physics**

11. A converging lens has a focal length of 20 cm in air. It is made of a material of refractive index 1.6. If it is immersed in a liquid of refractive index 1.3, what will be its new focal length?

12. Red light is incident on a thin converging lens of focal length ‘f’. Briefly explain how the focal length of the lens will change, if red light is replaced with blue light.

13. 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.**

14. 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.

15. An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size.

16. An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. 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.

17. A doctor has prescribed a corrective lens of power + 1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging?18. State the New Cartesian Sign Convention for lenses.

19. Write down the magnification formula for a lens in terms of object distance and image distance. How does it differ from the corresponding formula for a mirror?

20. A convex lens produces an inverted image magnified three times of an object placed at a distance of 15 cm from it. Calculate focal length of the lens.

21. a) Name the type of mirror used in (i) headlight of a car, (ii) rear view mirror of a bus. Justify your choice by giving reason.

b) When sunlight is concentrated at a paper placed at the principal focus of a convex lens, what happens to the paper? Why?

c) Observe carefully the figures (a) and (b) and tell which media is optically denser and why?

**ANSWERS (Basic Level)**

1. 10 cm & 20 cm 2. No

3. 2.12 × 108 m/sec 4. 1.33

6. 15 cm 7. (a) –10 cm (b) –10D

8. 20 cm 9. 50 cm

10. 30 cm 11. 52 cm

12. Fr > Fb i.e., focal length decreases.

13. (a) Concave, (b) Convex (c) Concave.

14. Yes

15.8.6 cm, virtual and erect and diminished (2.2 cm)

16. 54 cm, 14 cm, magnified, real and inverted

17. + 0.67 m, convex lens. 20. 11.25 cm

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