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  4. If two +5 D , lenses are mounted at some distance apart, the equivalent power will always be negative, if the distance is

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Q. If two $+5 \, D$ , lenses are mounted at some distance apart, the equivalent power will always be negative, if the distance is

NTA AbhyasNTA Abhyas 2020Ray Optics and Optical Instruments

Solution:

When two lenses are separated by some distance $x$ , then equivalent power
$P=P₁+P₂-xP₁P₂$
$\therefore P=5+5-x\times 5\times 5$
$or \, P=10-25x$
Power $P$ will be negative if 10-25x will be negative
$ie, \, 25x>10$
$or \, \, x>\frac{10}{25}$
$or \, \, x>\frac{10}{25}\times 100 \, cm$
$or \, \, x>40 \, cm$