Question

A pill bottle 3.0cm is placed 12cm in front of a mirror.An upright image 9.0cm tall is formed. What kind of mirror is it, and what is its radius radius of curvature?


Plzzzzzz Very fastttt​

Answer 1

Your Answer:

The type of mirror is concave

Radius = 36cm

Given:-

$\tt \blacktriangleright h_1 = 3cm \\\\ \tt \blacktriangleright h_2 = 9cm \\\\ \tt \blacktriangleright u= -12 cm$

Solution:-

$\tt Magnification \ \ in \ \ Mirror= \dfrac{h_i}{h_o} = -\dfrac{v}{u} \\\\ \tt \Rightarrow Magnification = \dfrac{9}{3} = 3 \\\\ \\Since \ \ image \ \ is \\\\ \ \ magnified \ \ and \ \ the \ \ the \ \ image \ \ formed \ \ is \ \ on \ \ right side \\\\ \ \ of \ \ mirror, Mirror \ \ is \ \ concave$

Now to calculate Radius, we have to find focal length first.

And to find image distance

$\tt -\dfrac{v}{-12} = 3 \\\\ \tt \Rightarrow v = 36cm$

So,

$\tt \dfrac{1}{v}+\dfrac{1}{u}= \dfrac{1}{f} \\\\ \Rightarrow \dfrac{1}{36} -\dfrac{1}{12} = \dfrac{1}{f} \\\\ \tt \Rightarrow \dfrac{-2}{36} = \dfrac{1}{f} \\\\ \tt \Rightarrow f =-18cm$

And we also know

$\tt 2f=R \\\\ \tt \Rightarrow 2(-18)=R \\\\ \tt \Rightarrow -36cm = R$

So, Radius is 36cm