In a concave mirror experiment,an object is p | vedclass

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(B) According to Newton's formula for mirrors,when distances are measured from the focus,the relationship is given by $x_1 x_2 = f^2$,where $x_1$ is t

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$\sqrt {{x_1}{x_2}} $

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(B) According to Newton's formula for mirrors,when distances are measured from the focus,the relationship is given by $x_1 x_2 = f^2$,where $x_1$ is the distance of the object from the focus and $x_2$ is the distance of the image from the focus.Alternatively,using the mirror formula $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$:Let the object distance be $u = -(f + x_1)$ and the image distance be $v = -(f + x_2)$.Substituting these into the mirror formula:$\frac{1}{-(f + x_2)} + \frac{1}{-(f + x_1)} = -\frac{1}{f}$$\frac{1}{f + x_2} + \frac{1}{f + x_1} = \frac{1}{f}$$\frac{(f + x_1) + (f + x_2)}{(f + x_1)(f + x_2)} = \frac{1}{f}$$f(2f + x_1 + x_2) = (f + x_1)(f + x_2)$$2f^2 + f x_1 + f x_2 = f^2 + f x_1 + f x_2 + x_1 x_2$$f^2 = x_1 x_2$$f = \sqrt{x_1 x_2}$

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

Similar Questions

The focal length of a concave mirror is $50 \ cm$. At what distance (in $cm$) should an object be placed to obtain a real and inverted image of double the size?

Write the relationship between the radius of curvature and the focal length for a spherical mirror.

$A$ convex mirror of focal length $f$ is placed at the origin with its reflecting surface towards the negative $x-$ axis. Choose the correct graph between $v$ and $u$ for $u < 0$.

Assertion : The formula connecting $u, v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.
Reason : Laws of reflection are strictly valid for plane surfaces,but not for large spherical surfaces.

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