The distance between an object and a screen is 100 cm. A lens can… | JEE Main 2020 (4 Sep, Shift 2)

Q88JEE Main 2020 · 4 SEP · SHIFT 2Medium

Spherical Surfaces & Thin Lenses

The distance between an object and a screen is 100 cm. A lens can produce real image of the object on the screen for two different positions between the screen and the object. The distance between these two positions is 40 cm. If the power of the lens is close to $\left( \frac{N}{100} \right) D$ where N is an integer, the value of N is _________.

Numerical answer type. Work it out, then open the answer.

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Answer: 476

Displacement method: $f = \frac{D^2 - x^2}{4D}$ with $D = 100$ cm, $x = 40$ cm.
$f = \frac{10000 - 1600}{400} = 21$ cm
$P = \frac{100}{21} \approx 4.76$ D $= \frac{476}{100}$ D
$N = 476$

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