Question

Figure shows a thin convex lens of focal length
20 cm with its optical centre at (50 cm, 0) and
principal axis along X-axis. If co-ordinates of a point
object is (20 cm, 5 cm), then co-ordinates of its image formed by lens will be
1. (100cm, 25cm)
2. (150cm,-25cm)
3. (60cm,-10cm)
4. (110cm,-10cm)​

Answer 1

option (4) (110cm,-10cm) is correct choice.

explanation : focal length of convex lens , f = +20cm

position of optical centre is (50cm, 0)

position of object in co-ordinate system is (20cm,5cm)

so, object distance, u = -(50cm - 20cm) = -30cm

size of object, h_o = +5cm

now using formula, 1/v - 1/u = 1/f

⇒1/v - 1/-30 = 1/1/20

⇒1/v = 1/20 - 1/30 = 1/60

⇒v = +60cm

so, position of image = +60cm + 50cm = 110cm

now magnification , m = v/u = height of image/height of object

⇒60/-30cm = height of image/5cm

⇒height of image = -10cm [ negative sign shows image form below the x-axis]

so, co-ordinate of its image is (110cm,-10cm).

option (4) is correct choice.

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Answer 2

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4. (110cm,-10cm)