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Question

The figure shows the graph between the image distance $$v$$ (in cm) and the object distance $$u$$ (in cm) for a thin convex lens. The focal length of the lens is
1542213_d7efdf6cda4c4eda9c9544d455859068.png


A
(5.00±0.05)cm
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B
(5.00±0.10)cm
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C
(10.0±0.10)cm
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D
(0.50±0.05)cm
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Solution

The correct option is B $$(5.00\pm 0.05)cm$$
The formula for a convex mirror-
$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$
Here, we put $$v =  + 10{\text{ cm}}$$ and $$u =  - 10{\text{ cm}}$$-
$$\frac{1}{f} = \frac{1}{{ + 10}} - \frac{1}{{ - 10}}$$
$$\therefore f =  + 5{\text{ cm}}$$
From the graph, we can see that $$\Delta u = 0.1$$ and $$\Delta v = 0.1$$
Differentiating the mirror formula, we obtain-
$$\frac{{\Delta f}}{{{f^2}}} = \frac{{\Delta v}}{{{v^2}}} + \frac{{\Delta u}}{{{u^2}}}$$
$$\Delta f = \left( {\frac{{\Delta v}}{{{v^2}}} + \frac{{\Delta u}}{{{u^2}}}} \right).{f^2}$$
$$\Delta f = \left( {\frac{{0.1}}{{{{10}^2}}} + \frac{{0.1}}{{{{10}^2}}}} \right) \times {5^2}$$
$$\Delta f = 0.05$$
Therefore, the focal length of the lens is $$(5 \pm 0.05){\text{ cm}}$$


Physics
NCERT
Standard XII

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