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  4. When an object is at distance x and y from a lens, a real image and a virtual image are formed respectively having the same magnification. The focal length of the lens is

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Q. When an object is at distance $x$ and $y$ from a lens, a real image and a virtual image are formed respectively having the same magnification. The focal length of the lens is

NTA AbhyasNTA Abhyas 2020Ray Optics and Optical Instruments

Solution:

The given lens is a convex lens. Let the magnification be m, then for real image using lens formula
$\frac{1}{m x}+\frac{1}{x}=\frac{1}{f}$ .......(i)
And for virtual image
$\frac{1}{- m y}+\frac{1}{y}=\frac{1}{f}$ ........(ii)
From equation (i) and equation (ii),
we get $f=\frac{x + y}{2}$