A concave mirror has a focal length of 20 cm. At what distance from the mirror should a 4 cm tall object be placed so that it forms an image at a distance of 30 cm from the mirror ? Also calculate the size of the image formed.

A concave mirror has a focal length of 20 cm. At what distance from th

1.	A concave mirror has a focal length of 20 cm. At what distance from the mirror should a 4 cm tall object be placed so that it forms an image at a distance of 30 cm from the mirror ? Also calculate the size of the image formed.
Answer» Solution :As per question, focal length of CONCAVE MIRROR f = - 20 cm, height of object h = + 4 cm and distance of image v = 30 cm. Following two cases may arise here : Case I : If the image formed is REAL then v = - 30 cm and so from mirror formula `(1)/(v) + (1)/(u) = (1)/(f)`, we have `(1)/(u) = (1)/(f) - (1)/(v) = (1)/((-20)) - (1)/((-30)) = (-1)/(20) + (1)/(30) = - (1)/(60) rArr u = - 60` cm and `h. = - (v)/(u) xx h = - ((-30))/((-60)) xx (+4) = - 2` cm So the object be placed 60 cm in front of mirror and image is an inverted image of size 2 cm. Case II : If the image formed is VIRTUAL then v = + 30 cm and now `(1)/(u) = (1)/(f) - (1)/(v) = (1)/((-20)) - (1)/((+30)) = (-1)/(20) - (1)/(30) = - (1)/(12) rArr u = - 12` cm and `h. = - (v)/(u) xx h = - ((+30))/((-12)) xx (+4) = + 10` cm So the object is placed at 12 cm in front of mirror and image is an erect image of height 10 cm.