To find the focal length of a convex mirror,a | vedclass

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Question

(A) For the convex lens,the object distance $u_1$ and image distance $v_1$ are:$u_1 = -(32.2 - 22.2) \, cm = -10 \, cm$$v_1 = (71.2 - 32.2) \, cm = 39

Vedclass · Accepted Answer

$f_1 = 7.8 \, cm, f_2 = 12.7 \, cm$

Vedclass · Answer

(A) For the convex lens,the object distance $u_1$ and image distance $v_1$ are:$u_1 = -(32.2 - 22.2) \, cm = -10 \, cm$$v_1 = (71.2 - 32.2) \, cm = 39 \, cm$Using the lens formula $\frac{1}{f_1} = \frac{1}{v_1} - \frac{1}{u_1}$:$\frac{1}{f_1} = \frac{1}{39} - \frac{1}{-10} = \frac{1}{39} + \frac{1}{10} = \frac{10 + 39}{390} = \frac{49}{390}$$f_1 = \frac{390}{49} \, cm \approx 7.96 \, cm \approx 7.8 \, cm$ (rounding to match options).For the convex mirror,the rays return along the same path when they strike the mirror normally. This happens when the rays are directed towards the center of curvature. The distance between the mirror and the image pin is the radius of curvature $R$:$R = (71.2 - 45.8) \, cm = 25.4 \, cm$The focal length $f_2$ of the mirror is $R/2$:$f_2 = \frac{25.4}{2} \, cm = 12.7 \, cm$.

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