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Question

In a concave mirror experiment, an object is placed at a distance $$x_1$$ from the focus and the image is formed at a distance $$x_2$$ from the focus. The focal length of the mirror would be :


A
x1x2
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B
x1x2
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C
x1+x22
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D
x1x2
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Solution

The correct option is C $$\dfrac{x_1+x_2}{2}$$
Given $$u=(f+x_{1})$$ and $$v=(f+x_{2})$$
The focal length $$f=\dfrac{uv}{u+v}=\dfrac{(f+x_{1})(f+x_{2})}{(f+x_{1})+(f+x_{2})}$$
On solving, we get
 $$f^{2}=x_{1}x_{2}$$ or $$f=\sqrt{x_{1}x_{2}}$$

Physics

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