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Ray Optics and Optical Instruments — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsRay Optics and Optical Instruments5 Marks
Question
A converging mirror M1, a point source S and a diverging mirror M2 are arranged as shown in figure. The source is placed at a distance of 30cm from M1. 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 M2.

✓

Answer


  1. As shown in figure, for 1st reflection in M1, u = -30cm, f = -20cm

$\Rightarrow\frac{1}{\text{v}}+\frac{1}{-30}=-\frac{1}{20}\Rightarrow\text{v}=-60\text{cm}.$

So, for 2nd reflection in M2

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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