SPHERICAL MIRRORS 9.pptx BY KAVYA SINGH CLASS 9

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KAVYA SINGH

1. SPHERICAL MIRRORS BY KAVYA SINGH CLASS 9 TH D ROLL NO. 23

2. OPTICAL DEVICES A lens is an optical device that is used to bend light in a specific way. A converging lens bends light so that the light rays come together to a point. A diverging lens bends light so it spreads light apart instead of coming together. Mirrors reflect light and allow us to see ourselves. A prism is another optical device that can cause light to change directions. A prism is a solid piece of glass with flat polished surfaces.

3. SPHERICAL MIRRORS Spherical Mirror : A curved mirror formed by a part of a hollow glass sphere with a reflecting surface. TWO TYPES OF SPHERICAL MIRRORS : Concave mirror : A concave mirror is a curved mirror with the reflecting surface on the hollow side. Convex mirror : A convex mirror is a curved mirror with the reflecting surface on the outer side.

4. TYPES OF SPHERICAL MIRRORS

5. Centre of Curvature : The centre of curvature of a curved mirror is defined as the center of the hollow glass sphere of which the curved mirror was {previously} a part. Radius of curvature : The radius of the hollow glass sphere of which the spherical mirror was a part. Principal Axis: The imaginary line passing through its pole P and center of curvature C. Pole: The pole is defined as the geometric center of the curved mirror.

6. Focus : The principal focus is defined as the point on the principal axis where the light rays travelling parallel to the principal axis after reflection actually meet .

7. Focal length The focal length is the distance between the pole P Principal focus F of a curved mirror. The focal length is half the radius of curvature . FOCAL LENGTH = RADIUS OF CURVATURE

8. FOCAL length = Radius of curvature /2 To show that f = R/2 for a Concave Mirror Let a ray of light AB be incident, parallel to the principal axis, on a concave mirror. After reflection, the ray AB passes along BD, through the focus F. BD is normal to the concave mirror at B. Angle ABC = Angle CBD-------------------- (1) We know that AB and PC are parallel to each other. Angle ABC =Angle BCP--------------------(2)

9. From equation (1) and (2) we get Hence triangle BCF is isosceles BF = CF----(3) If the aperture of the mirror is small then B will be very close to P. BF=PF-----(4) From equation 3 and 4 CF=PF PC=PF + CF => PC= 2 PF BY definition PF= f (focal length) and PC= R (RADIUS OF CURVATURE) Then, R =2f i.e. Focal length = Radius of curvature/2.

10. Sign convention for spherical mirrors The object is always placed on the left of the mirror and light from the object falls from the left to the right. All distances parallel to the principal axis are measured from the pole. All distance measured to the right of the pole are taken as + ve . All distance measured to the left of the pole are taken as – ve . The height measured upwards perpendicular axis is taken as + ve . The height measured downwards perpendicular to the principal axis is taken as – ve .

11. Sign convention for spherical mirrors

12. Mirror formula Mirror formula is the relationship between object distance [u], image distance [v] and focal length. Mirror formula of the Concave Mirror is 1/f =1/v + 1/u Here and object AB at a distance u from the pole. The image A’B’ is formed at a distance v from the mirror. The position of the image is obtained by drawing a ray diagram.

13. MIRROR FORMULA

14. In angle ABC and angle A’B’C both are a similar triangle SO, AB/A’B, = BC/B’C ---------{1} Similarly , Angle DEF ~ Angle A’B’C DE/A’B’ = EF/ B’F But, DE/ A’B’ = EF/B’F But, DE = AB So, AB/A’B’ = EF / B’F -----------{2}

15. From (1) and (2) BC/B’C = EF/ B’F If D is very close to P then EF = PF BC/ B’C = PF/B’F We know , BC=PC – PB and B’C= PC B’F = PB’ – PF PC – PB /PB’ – PC = PF / PB’ – PF By sign convention PC = -R, PB = -u PF = -f and PB’ = -v

16. Images formed by concave mirror When the object is at infinity the image is formed at the focus , it is highly diminished, real and inverted.

17. When the object is beyond C, the image is formed between C and F, it is diminished , real and inverted.

18. When the object is between C and F , the image is formed beyond C , it is enlarged, real and inverted.

19. When the object is at F, the image is formed at infinity, it is highly enlarged, real and inverted.

20. When the object is between F and P, the image is formed behind the mirror, it is enlarged, virtual and erect.

21. Uses of concave mirrors Concave mirrors are used in torches, search lights and head lights of vehicles to get parallel beams of lights. They are used as shaving mirrors to see larger image of the face. They are used by dentists to see larger images of teeth. Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces.

22. Images formed by convex mirror When the object is at infinity, the images is formed at F behind the mirror , it is highly diminished, virtual and erect.

23. When the object is between infinity and pole, the image is formed behind the mirror, it is diminished, virtual and erect.

24. USES OF CONVEX MIRRORS Convex mirror are used as rear- view mirror in vehicles. Convex mirrors give erect diminished images of objects. They also have a wider field of view than plane mirrors.