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  • With a concave mirror, an object is placed at a distance  from the principal focus, on th

With a concave mirror, an object is placed at a distance x_1 from the principal focus, on the principal axis. The image is formed at a distance x_2 from the principal focus. The focal length of the mirror is:

Option: 1

x_1.x_2


Option: 2

\frac{x_1 + x_2}{2}


Option: 3

\sqrt{x_1. x_2}


Option: 4

\sqrt{\frac{x_1}{x_2}}


Answers (1)

best_answer

 

 

Newton's Formula -

Newton's Formula:

As we know that the mirror formula is given as 

\frac{1}{v}+\frac{1}{u}=\frac{1}{f}

Let's assume, x = distance of the object from focus 

                       y =  distance of the image from focus 

Newton's formula is useful  for calculating the image position for a curved mirror.

The diagram shows the position of an object and its image formed by a concave mirror.

Let the distances of the object and image from the principal focus of the mirror be x and y respectively.

Then: Object distance (u) = f+x and Image distance (v) = f+y

Using the mirror formula \frac{1}{v}+\frac{1}{u}=\frac{1}{f}  we have: \frac{1}{f+x}+\frac{1}{f+y}=\frac{1}{f}   

and simplifying this we get:    \boxed{f^2= xy }

 

-

 

 

Posted by

Ajit Kumar Dubey

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