A convex lens of focal length 15 cm is split into two halves and the two halves are placed at a separation of 120 cm. Between the two halves of convex lens a plane mirror is placed horizontally and at a distance of 4 mm below the principal axis of the lens halves. An object AB of length 2 mm is placed at a distance of 20 cm from one half lens as shown in figure. The final image of the point A is formed at a distance of from the principal axis. Determine the value of n.

Engineering

Physics

Curved Surface Refraction

Reflection at Plane Surface New

Question

A convex lens of focal length 15 cm is split into two halves and the two halves are placed at a separation of 120 cm. Between the two halves of convex lens a plane mirror is placed horizontally and at a distance of 4 mm below the principal axis of the lens halves. An object AB of length 2 mm is placed at a distance of 20 cm from one half lens as shown in figure. The final image of the point A is formed at a distance of $\frac{n}{3} mm$ from the principal axis. Determine the value of n.

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The first half-lens forms the image A'B' (= 6mm).

$∴ \frac{1}{v} - \frac{1}{- 20} = \frac{1}{15} \Rightarrow v = + 60 cm$

$∴$ m₁ = –3

the plane mirror forms the image A"B" with A" located 8 mm below the principal axis. The second half lens forms the image A'''B'''. Now

u = –60 m

⇒ v = +20 cm

$∴ m_{2} = - \frac{1}{3}$

$∴$ A''' is located at 8/3 mm above the principal axis.

$∴$ n = 8