Two half convex lenses of focal lengths f₁ = 16 cm and f₂ = 21 cm respectively are placed such that their principal axes coincide. Both the lenses form image of a real point object O on a fixed screen as shown. The distance between object and screen is 100 cm. Then pick up the correct statement(s)

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The distance of lens1 from object O can be 20 cm

The distance of lens 1 from object O can be 80 cm

The distance of lens 2 from object O can be 30 cm

The distance of lens 2 from object O can be 70 cm

answer is A, B, C, D.

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Detailed Solution

Let say distance between object and Lens 1 is 'x'

$\begin{array}{l} L e n s f o r m u l a f o r L e n s 1 : \\ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \\ \Rightarrow \frac{1}{(100 - x)} - \frac{1}{(- x)} = \frac{1}{(16)} \\ \Rightarrow x = 20 c m o r 80 c m \end{array}$

Similarly, let say distance between object and Lens 2 is ‘y’

$\begin{array}{l} L e n s f o r m u l a f o r L e n s 2 : \\ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \\ \Rightarrow \frac{1}{(100 - y)} - \frac{1}{(- y)} = \frac{1}{(21)} \\ \Rightarrow x = 30 c m o r 70 c m \end{array}$