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 ?

Explanation

(i) Here, `u = -30 cm, R = - 40 cm, v = ?`
From `(1)/(v) + (1)/(u) = (1)/(f) = (2)/(R )`
`(1)/(v) = (2)/( R) - (1)/(u) = (2)/(-40) + (1)/(30) = -(1)/(60)`
`v = - 60cm`, on the same side as object.
`:.` Distance of image from the object `= 60 - 30 = 30 cm`.
`m = (I)/(O) = (-v)/(u) = (+60)/(-30) = -2`, negative sign for inverted image.
(ii) Focal length `(f)` of mirror remains unaffected. On changing `u` , `v` changes and not `f`.
(iii) Mirror formula reveals that `f` depends only on `R`, and not `u` or `v`. Infact on changing `u` , `v` changes, but `f` remains constant.
In day to day life, `u` corresponds to a situation that arises and `v` corresponds to our response to the situation. We are like a mirror. Our nature/curvature determines our focal length. The mirror formula implies that our nature is not affected by the situation that comes up. Response to a particular situation will depend on our nature.