Question

A concave makeup mirror has a radius of curvature equal to 40 cm. How far away must your face be from the mirror so that your virtual image is twice the size of your actual face?.

Answer 1

Answer: 10 cm

Step-by-step explanation:

`$$The focal length is: \\ \\ \begin{aligned}f &=(R)/(2) \\&=-(46)/(2) \\f &=-20 \mathrm{~cm}\end{aligned}$$`

`$$ Since the image is virtual: \\ \\ :\begin{aligned}(v)/(u) &=m \\\Rightarrow & v=m u \\\Rightarrow &v=2 u\end{aligned}$$`

`$$ Using: \\ \\ \begin{aligned}&(1)/(l)=(1)/(v)+(1)/(u) \\&(1)/(20)=-(1)/(2 u)+(1)/(u) \\&(1)/(2 u)=(1)/(-20) \\&\Rightarrow u=-10 \\&\therefore u=10 \mathrm{~cm}\end{aligned}$$`

Therefore, you must be 10 cm away from the mirror so that your virtual image is twice the size of your actual face