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

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

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 $$(5 \pm 0.05){\text{ cm}}$$PhysicsNCERTStandard XII

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