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With a concave mirror, object is placed at an distance of 16 cm from principal focus on the pricipal axis.The image is formed at a distance 4cm from the principal focus. The focal length of the mirror is :

Option: 1

64 cm


Option: 2

10 cm


Option: 3

2 cm


Option: 4

8 cm


Answers (1)

best_answer

Newton's Formula -

XY = f^{2}

- wherein

X,Y = distance ( along the principal axis ) of the object and image respectively from the principal focus.

 

 Let X1 = 16 cm

X2 = 4 cm

u=f-x_{1}\Rightarrow \frac{1}{f-x_{2}}+\frac{1}{f-x_{1}}=\frac{1}{f}

v=f-x_{2}

or

\frac{1}{f}=\frac{2f-(x_{1}+x_{2})}{(f-x_{1})(f-x_{2})}

\Rightarrow f^{2}-(x_{1}+x_{2})f+x_{1}x_{2}=2f^{2}-(x_{1}+x_{2})f

\Rightarrow x_{1}x_{2}=f^{2}

f=\sqrt{16\times 4} cm =8 cm

  

 

 

Posted by

vishal kumar

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