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  • A thin cylindrical rod of length 10 cm is placed horizontally on the principle axis of a concave mirror of focal length 20 cm. The rod is placed in a such a way that mid point of the rod is

A thin cylindrical rod of length 10 cm is placed horizontally on the principle axis of a concave mirror
of focal length 20 cm. The rod is placed in a such a way that mid point of the rod is at 40 cm from the
pole of mirror. The length of the image formed by the mirror will be  \frac{x}{3}cm . The value of x is _______.

Option: 1

32


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Image of end A:
u = –35 cm
f = –20 cm
v = ?

\begin{aligned} & v=\frac{u f}{u-f} \\ & =\frac{-35 \times-20}{-35+20} \\ & =\frac{-35 \times-20}{-15} \end{aligned}

v=-\frac{140}{3}

Image of end B:
u = –45 cm
v = ?
f = – 20 cm

\begin{aligned} & v=\frac{u f}{u-f} \\ & =\frac{-45 \times-20}{-45+20} \\ & =\frac{-45 \times-20}{-25} \\ & v=-36 \\ \end{aligned}

\begin{aligned} & \therefore \text { length of image }=\left|-36+\frac{140}{3}\right| \\ & =\left|-\frac{108+140}{3}\right| \\ & =\frac{32}{3} \\ & \therefore \text { The value of } x=32 \\ & \end{aligned}

 

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Pankaj

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