Refraction by Spherical Surfaces: Practice Problem & Solution
A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is: (2011 Mains)
Solution Explained:
To solve this problem, we apply the core principles of Refraction by Spherical Surfaces. Understanding the underlying formula is key to arriving at the correct answer below:
Without the lens, the rays meet 5 cm closer, meaning the original convergence point was at $15 - 5 = 10 cm$. Thus, virtual object distance is $u = +10 cm$. The final image distance is $v = +15 cm$. Using the lens formula $1/f = 1/v - 1/u$, we get $1/f = 1/15 - 1/10 = (2 - 3)/30 = -1/30$. Therefore, $f = -30 cm$.
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