An object is placed Infront of a plane mirror 12 cm away from it. The object is kept fixed while the plane mirror is shifted towards the object by a distance of 4 cm. The length of shift in the position of image is equal to ___________ cm.
Correct Answer: 8
Approach Solution - 1
Step 1: Initial Distance Between Object and Image
For a plane mirror, the image is formed at the same distance behind the mirror as the object is in front of it.
Initially, the object is placed \( 12 \, \text{cm} \) away from the mirror. Therefore, the distance between the object and the image is:
\[ \text{Distance} = 2 \times 12 = 24 \, \text{cm} \]
Step 2: Final Distance After Shifting the Mirror
The mirror is shifted towards the object by \( 4 \, \text{cm} \), so the new distance between the object and the mirror becomes:
\[ 12 - 4 = 8 \, \text{cm} \]
Therefore, the distance between the object and the image is:
\[ \text{Distance} = 2 \times 8 = 16 \, \text{cm} \]
Step 3: Calculate the Shift in the Image Position
The shift in the image position is the difference between the initial and final distances between the object and the image:
\[ \text{Shift} = 24 - 16 = 8 \, \text{cm} \]
Conclusion:
The shift in the position of the image is 8 cm.
Answer: 8 cm
Approach Solution -2
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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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