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Geometrical Optics — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsGeometrical Optics5 Marks
Question
A converging mirror $M_1,$ a point source S and a diverging mirror $M_2$ are arranged as shown in figure. The source is placed at a distance of 30cm from $M_1$. The focal length of each of the mirrors is 20cm. Consider only the images formed by a maximum of two reflections. It is found that one image is formed on the source itself.
  1. Find the distance between the two mirrors.
  2. Find the location of the image formed by the single reflection from $M_2.$
✓

Answer


  1. As shown in figure, for $1^{st}$ reflection in $M_1, u = -30cm, f = -20cm$
$\Rightarrow\frac{1}{\text{v}}+\frac{1}{-30}=-\frac{1}{20}\Rightarrow\text{v}=-60\text{cm}.$
So, for $2^{nd}$ reflection in $M_2$
$u = 60 - (30 + x) = 30 - x$
$v = -x; f = 20cm$
$\Rightarrow\frac{1}{30-\text{x}}-\frac{1}{\text{x}}=\frac{1}{20}$
$\Rightarrow \frac{\text{x}-30+\text{x}}{\text{x}(30-\text{x})}=\frac{1}{20}$
$\Rightarrow40\text{x}-600=30\text{x}-\text{x}^2$
$\Rightarrow\text{x}^2+10\text{x}-600=0$
$\Rightarrow\text{x}=\frac{10\pm50}{2}=\frac{40}{2}=20\text{cm}$ or $-30\text{cm}$
$\therefore$ Total distance between the two lines is 20 + 30 = 50cm.

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