Answer:
a. 26.7 cm. b. 11.4 cm.
Step-by-step explanation:
a. We know h'/h = d'/d where h' = image height = + 2 cm (since it is a real image), h = object height = + 1.5 cm, d' = image distance from mirror and d = object distance from mirror = 20 cm
So, from h'/h = d'/d
d = h'd/h
= 2 cm × 20 cm/1.5 cm
= 40/1.5 cm
= 26.67 cm
≅ 26.7 cm
The position of the image is 26.7 cm from the mirror
b. Using the mirror formula
1/d + 1/d' = 1/f where d = object distance from mirror = + 20 cm, d' = image distance from mirror = + 26.7 cm (its positive since its a real image) and f = focal length of mirror.
So, 1/d + 1/d' = 1/f
⇒ f = dd'/(d + d')
= 20 cm × 26.7 cm/(20 cm + 26.7 cm)
= 534/46.7
= 11.43 cm
≅ 11.4 cm
The focal length of the mirror is 11.4 cm