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**Introductory Exercise 27.1**

**Ques 1: Show that the unit of is m/s.Sol:** = Speed of light in vacuum.

B

(a) What is the wavelength and frequency of the wave?

(b) Write an expression for the electric field vector.

Ans:

= 0.0125 m= 1.25 cm

= 2.39 Ã— 10

E

= (3 Ã— 10

kx and Ï‰t have same sign. Therefore, electromagnetic wave is travelling along negative x direction. are in mutually perpendicular direct ions. Hence oscillations of are along z-direction.

**Introductory Exercise 27.2**

**Ques 1: Prove that for any value of angle i, rays 1 and 2 are parallel.****Sol: **

PQ and MN are mutually parallel. Rays 1 and 2 are making equal angles (= âˆ i) from PQ and MN. So, they are mutually parallel.**Ques 2: A man approaches a vertical plane mirror at speed of 2 m/s. At what rate does he approach his image?****Sol: ****Ques 3: A pole of height 4 m is kept in front of a vertical plane mirror of length 2 m. The lower end of the mirror is at a height of 6 m from the ground. The horizontal distance between the mirror and the pole is 2 m. Up to what minimum and maximum heights a man can see the image of top of the pole at a horizontal distance of 4 m (from the mirror) standing on the same horizontal line which is passing through the pole and the horizontal point below the mirror?Sol:**

PQ = Pole

MN = Image of pole

Minimum height required = AD = BD + AD = 10m

Further,

Maximum height required = AE = BE+ AB = 16 m

**Introductory Exercise 27.3**

**Ques 1: Assume that a certain spherical mirror has a focal length of- 10.0 cm. Locate and describe the image for object distances of(a) 25.0 cm (b) 10.0 cm (c) 5.0 cm.Sol:** Apply

(a) f = -10 cm, u = - 25 cm Solving we get, v = -16.7cm

Since, v is negative, image is in front of mirror. So it is real. Similarly, we can solve for other parts.

(a) Describe the motion of ball's image in the mirror.

(b) At what time do the ball and its image coincide?

Sol:

From F to P, image is virtual.

At O

âˆ´

v = - 0.6 m

(b) When object is at C and P, image coincides with object. Using,

or **Ques 3: A spherical mirror is to be used to form on a screen 5.0 m from the object an image five times the size of the object.(a) Describe the type of mirror required.(b) Where should the mirror be positioned relative to the object?Sol: **(a) Image has to be taken on a screen. So it should be real. Hence mirror should be concave.

Image is 5 times magnified. Hence, | v | = 5 | u |

or

(5 + x) = 5x

Solving we get, x = 1.25 cm

Now using,

We have,

Solving we get, R = - 2.08 m

Sol:

Sol:

In Î”O

or

x = (20)(I

In Î”O

âˆ´

or (40 - x) = 40(I

Solving Eqs. (i) and (ii) we get,

Mirror Type | Radius | Focal Length | Object Distance | Image Distance | Lateral Magnification | Real/Virtual Image |

-25 | 40 | |||||

20 | -30 | |||||

+15 | +30 | |||||

20 | -2.0 | |||||

+20 | -40 | |||||

-10 | +2.0 |

**Sol: **Negative focal length means concave mirror and positive focal length means convex mirror.

Apply,

And

Further, if v is negative then image is in front of mirror. So, it is real and inverted.

R = 2f

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