A small candle 2.5 cm height is placed in front of a concave mirror of radius of curvature 36 cm at a distance 27 cm from the concave mirror.
i. At what distance from the mirror should a screen be placed in order to receive a sharp image ?
ii. Describe the nature and size of the image.
iii. If the candle is moved close to the mirror, what will be the position of the screen ?

Explanation

`h_(0) = 2.5 cm, R = 36 cm , f = (R)/(2) = ~ 18` cm , u = - 27 cm
i. `(1)/(f) = (1)/(u) + (1)/(v) " " (1)/(v) = (1)/(f) - (1)/(u) " " = (1)/(-18) - (1)/(-27)`
v = - 54 cm
The negative sign indicates that image is formed in front of mirror (on the same side as that of the object ) `therefore` screen should be placed at a distance of 54 cm in front of the mirror .
ii. m = `(h_(i))/(h_(0)) = (-v)/(u) " " h_(i) = (-v)/(u) xx h_(0) = (-54)/(27 ) xx 2.5 = - 5 cm `
Image is magnified. Negative sign shows that image is real and inverted .
iii. If the candle is moved closer to the mirror, then u decreases and v increases. hence screen has to be moved farther and farther. When u `lt` 18 cm, image formed will be virtual and hence can.t be formed on the screen .