A thin convex lens of focal length 30 , cm fo | vedclass

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Question

(D) The convex lens forms an image of an object at infinity at its focal point. The distance of this image $(I_{1})$ from the convex lens is $30 \, cm

Vedclass · Accepted Answer

$2.5$

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(D) The convex lens forms an image of an object at infinity at its focal point. The distance of this image $(I_{1})$ from the convex lens is $30 \, cm$.Since the concave lens is placed $26 \, cm$ from the convex lens,the image $I_{1}$ acts as a virtual object for the concave lens.The distance of this virtual object from the concave lens is $u = +(30 - 26) \, cm = +4 \, cm$.For the concave lens,the focal length $f = -20 \, cm$.Using the magnification formula $m = \frac{f}{f + u}$,we have:$m = \frac{-20}{-20 + 4} = \frac{-20}{-16} = 1.25$.Since $m = \frac{h_{i}}{h_{0}}$,where $h_{0} = 2 \, cm$ is the height of the object $I_{1}$ (which is the image formed by the first lens),$h_{i} = m 	imes h_{0} = 1.25 	imes 2 = 2.5 \, cm$.

$A$ thin convex lens of focal length $30 \, cm$ forms an image $2 \, cm$ high,of an object at infinity. $A$ thin concave lens of focal length $20 \, cm$ is placed $26 \, cm$ from the convex lens on the side of the image. The height of the final image is.....$cm$.

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