From a thin convex lens of focal length F = 20 cm and aperture diameter of 10 mm a small piece was cut as shown in the figure. The piece is then placed in contact with the remaining part of the lens o

Question

From a thin convex lens of focal length $F = 20 cm$ and aperture diameter of 10 mm a small piece was cut as shown in the figure. The piece is then placed in contact with the remaining part of the lens on the original principal axis of the lens. If the optical centre of the original lens is taken to be origin of co-ordinates and a point object is placed at (-30, 0), then the image coordinate becomes (x, y). Find the value of x + y (both 'x' and 'y' are in the lowest fractional form)

TestHub · Accepted Answer

First refraction: v 1 ​ − − 30 1 ​ = 20 1 ​ ⇒ v = + 60 c m Second refraction (cut piece): v 1 ​ − 60 1 ​ = 20 1 ​ ⇒ v = + 15 c m The second lens axis is 3 mm below the original axis, so the object is 3 mm above it: h i ​ = 60 15 ​ × 3 = 4 3 ​ mm Image coordinate: y = − ( 3 − 4 3 ​ ) = − 4 9 ​ mm , i.e. (15, -9/4). x + y = 15 − 4 9 ​ = 4 51 ​ = 12.75

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