Here, `u =` distance of candle flame from the lens
`= 50.0 - 12.0 = 38 cm = -38 cm` (as per New Cartesian Sign Convention)
`v =` distance of screen from the lens
`= 88.0 - 50.0 = 38 cm` (as per new Cartesian Sign Convention)
(i) From `(1)/(f) = (1)/(v) - 1/u`
`(1)/(f) = 1/38 + 1/38 = 2/38, f = 38/2 = 19 cm`.
(ii) When the student shifts the candle towards the lens at a position of `31.0 cm`,
` u = 50.0 - 31.0 = 19 cm`.
The candle lies at the focus of convex lens.
The image will be formed at infinity.
(iii) When he further shifts the candle towards the lens, the candle lies between optical centre of the lens and its focus. Therefore, the image formed is virtual, erect and magnified.
(iv) For ray diagram in case (iii) above