Rohit focussed the image of a candle flame on a white screen using a convex lens. He noted position of candle `= 26.0 cm`, position of convex lens `= 50.0 cm` and position of screen `= 74.0 cm`.
(i) What is focal length of convex lens?
(ii) Where will the image be formed if he shifts the candle towards the lens at a position of 38 cm ?
(iii) Draw a ray diagram to show the formation of image in (ii) above.

Explanation

(i) Here, `u = "distance of candle from convex lens" = - (50.0 - 26.0) = - 24.0 cm`
`v =` distance of screen from convex lens `= (74.0 - 50.0) = 24.0 cm`
From lens formula
`(1)/(f) = (1)/(v) - 1/u = 1/24 -1/(-24) = 1/12`
`f = 12 cm`
(ii) When position of candle is shifted to 38 cm, `u = - (50.0 - 38.0) = -12.0 cm`
`(1)/(v) - 1/u = (1)/(f)`
`(1)/(v) = (1)/(f) + 1/u = 1/12 - 1/12 = 0, v = oo`
The image will be formed at infinity.

(iii) The course of rays is shown Fig.