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| Relation Between f and R |
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| To show that f = R/2 where f is the focal
length of a mirror and R its radius of curvature. |
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| To Show that f = R/2 for a Concave Mirror |
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| 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. BC is normal to the concave mirror at B. |
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| We know that AB and PC are parallel to each other. |
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| From equations (1) and (2) we get |
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| Hence triangle BCF is isosceles |
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 BF = CF --------- (3) |
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| If the aperture of the mirror is small then B will be very close to P. |
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 BF = PF --------- (4) |
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| From equations (3) and (4) we conclude that |
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| But by definition PF = f (focal length) and PC = R (radius of curvature) |
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| Note: While Deriving the Relation we
have considered only one of the incident rays |
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| Let a ray of light AB be incident, parallel to the principal axis, on a convex mirror. After reflection the ray AB appears to come from F. BC is the normal to the convex mirror at B. |
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| From equations (2) and (3) |
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| Hence triangle BCF is isosceles |
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 BF = CF ------- (4) |
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| If the aperture of the mirror is small then B will be very close to P. |
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 BF = PF ------- (5) |
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| From equations (4) and (5) we conclude that |
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| By definition PF = f (focal length) and |
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| PC = R (radius of curvature) |
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| From the above relation we conclude that the radius of curvature of a mirror is twice its focal length. |
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