Question:

An object moving at a speed of 5m/s 5\,m/s towards a concave mirror of focal length f=1m f = 1\, m is at a distance of 9m 9\, m . The average speed of the image is

Updated On: Jun 14, 2022
  • 15m/s \frac{1}{5}\, m/s
  • 110m/s \frac{1}{10}\, m/s
  • 59m/s \frac{5}{9}\, m/s
  • 49m/s \frac{4}{9}\, m/s
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The Correct Option is A

Solution and Explanation

According to mirror formula
1f=1v+1u\frac{1}{f}=\frac{1}{v}+\frac{1}{u}
Here u=9mu=-9\,m and f=1mf=-1\,m
1(1)1(9)=1v\frac{1}{(-1)}-\frac{1}{(-9)}=\frac{1}{v}
v=98m\Rightarrow v=\frac{-9}{8}\,m
As the object moves at a constant speed of 5m/s5 \,m/s after 1s1 \,s the new position of image is
u=9m+5m=4mu'=-9m+5m=-4m
1(1)1(4)=1v\therefore \frac{1}{(-1)}-\frac{1}{(-4)}=\frac{1}{v'}
v=43m\Rightarrow v'=\frac-{4}{3}\,m
The shift in the position of image in 1s1s is
vv=98+4315v-v'=\frac-{9}{8}+\frac{4}{3} \approx\frac{1}{5}
\therefore Average speed of image =15m/s=\frac{1}{5}\,m/s
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Concepts Used:

Ray Optics and Optical Instruments

Optics, deals with the determination of behaviour and the properties of light, along with its interactions with the matter and also with the instruments that are used to detect it.

Ray optics is also known as the geometrical optics and it is a branch of science which describes light propagation.

Reflection is the change in direction of light at an interface in-between two different media so that the wave-front returns into a medium from which it was originated.

Speed of light is the rate at which the light travels in free space.

A phenomenal change in image formed when the light is passed from one medium to another which is called Refraction.

Total Internal Reflection is the reflection of light when the light ray enters into a rarer medium from a denser medium and the angle of incidence is higher than the critical angle of incidence then that light ray will be reflected back to the denser medium.

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