Prove that spherical mirror formula is applicable equally to a plane mirror.
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The shperical mirror formula is `(1)/(f) = (2)/(R ) = (1)/(v) + (1)/(u)` For a plane mirror, `R = oo` `:. 1(v) + (1)/(u) = (2)/(oo) = 0 or (1)/(v) = -(1)/(u) or = v = -u` As `u` is negative , `v` must be positive. Hence image in a plane mirror is formed behind the mirror at the same distance as the object is in front of it. This is what we find in a plane mirror. Hence the desired result.
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The formula governing reflection of light from a spherical mirror is (1)/(v) + (1)/(u) = (2)/(R ) , where u = distance of object from pole of mirror, upsilon = distance of image from pole of mirror f = focal length of mirror, R = radius of curvature of mirror. This is known as mirror formula and is applicable equally to concave mirror and convex mirror. m = (I)/(O) = (upsilon)/(u) Read the above passage and answer the following questions : (i) An object is held at a distance of 30 cm in front of a concave mirror of radius of curvature 40 cm . Calculate distance of the image from the object ? What is linear magnification of the mirror ? (ii) The object is moved to a distance of 40 cm in front of the mirror. How is focal length of mirror affected ? (iii) What values of life do you learn from the mirror formula ?
