In an optical bench experiment, the index err | vedclass

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Question

(B) The index error is defined as the difference between the observed distance and the actual distance. Actual distance $u = u_{obs} - (	ext{index er

Vedclass · Accepted Answer

$5.54$

Vedclass · Answer

(B) The index error is defined as the difference between the observed distance and the actual distance. Actual distance $u = u_{obs} - (	ext{index error}) = 9 - 1 = 8 \, cm$. Actual distance $v = v_{obs} - (	ext{index error}) = 17 - (-1) = 18 \, cm$. Using the lens formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$. Here, by sign convention, $u = -8 \, cm$ and $v = +18 \, cm$. $\frac{1}{f} = \frac{1}{18} - \frac{1}{-8} = \frac{1}{18} + \frac{1}{8}$. $\frac{1}{f} = \frac{4 + 9}{72} = \frac{13}{72}$. $f = \frac{72}{13} \approx 5.538 \, cm \approx 5.54 \, cm$.

In an optical bench experiment, the index error is $+1 \, cm$ and $-1 \, cm$ between the object needle and lens, and between the lens and image needle, respectively. The observed values of $u$ and $v$ are $9 \, cm$ and $17 \, cm$. The focal length of the lens is ..... $cm$.

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