A thin double-convex lens is intended to focus the image of an object onto a screen so that the image is life-sized on the screen. The lens has equal-magnitude radii of $83 \mathrm {~cm}$ and a refractive index of 1.6.
(a) What is the distance $d$ from the image to the screen?
(b) What is the total distance $L$ between the object and the image?
A) (a) $d = 69 \mathrm {~cm}$
(b) $L = 35 \mathrm {~cm}$
B) (a) $d = 138 \mathrm {~cm}$
(b) $L = 276 \mathrm {~cm}$
C) (a) $d = - 138 \mathrm {~cm}$
(b) $L = - 276 \mathrm {~cm}$
D) $( \mathrm { a } ) d = 276 \mathrm {~cm}$
(b) $L = 552 \mathrm {~cm}$

Question

Quizplus · Accepted Answer

For a life-sized image, the magnification (M) is 1. The lens maker's formula, $1/f = (n-1)(1/R_1 - 1/R_2)$, where $n$ is the refractive index and $R_1$ and $R_2$ are the radii of curvature, is used to find the focal length $f$. Given $R_1 = 83 \, \text{cm}$, $R_2 = -83 \, \text{cm}$ (since it's double-convex and the radii have opposite signs), and $n = 1.6$, we find $f = 69 \, \text{cm}$. For a life-sized image, the object and image distances from the lens must both be twice the focal length, so $d = 2f = 138 \, \text{cm}$, and the total distance $L = 2d = 276 \, \text{cm}$.

A Thin Double-Convex Lens Is Intended to Focus the Image 83 cm83 \mathrm {~cm}83 cm

A Thin Double-Convex Lens Is Intended to Focus the Image $83 \mathrm {~cm}$