Option 2 : 36 cm away from the mirror
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Concept-
- The optical instrument which reflects the light and make the image of the object is called as mirror.
- The mirror having spherical curved reflecting surface is called as spherical mirror.
There are two types of spherical mirror:
1. Concave mirror:
- The spherical mirror having inward reflecting surface is called as concave mirror.
- The images form by the concave mirror can be real as well as virtual.
2. Convex mirror:
- The mirror whose reflecting surface is outward is called as convex mirror.
- The images form by the convex mirror is always virtual.
The mirror formula is given by:
\(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\)
Where u is object distance, v is image distance and f is focal length of the mirror
Explanation-
Given that:
Object distance (u) = - 40 cm
Focal length of the concave mirror (f) = - 15 cm
Use mirror formula:
\(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\)
\(\frac{1}{{ - 40}} + \frac{1}{v} = \frac{1}{{ - 15}}\)
\(\frac{1}{v} = \frac{1}{{40}} - \frac{1}{{15}} = \frac{{3 - 8}}{{120}} = \frac{{ - 5}}{{120}} = - \frac{1}{{24}}\)
Image distance (v) = - 24 cm
Now object is displaced through a distance of 20 cm towards the mirror;
New object distance (u’) = - (40 - 20) = - 20 cm
Focal length (f) = -15 cm
Use mirror formula:
\(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}\)
\(\frac{1}{{ - 20}} + \frac{1}{{v'}} = \;\frac{1}{{ - 15}}\)
\(\frac{1}{{v'}} = \frac{1}{{20}} - \frac{1}{{15}} = \frac{{3 - 4}}{{60}} = - \frac{1}{{60}}\)
New image distance (v’) = - 60 cm
Displacement of the image = |v’| - |v | = 60 - 24 = 36 cm away from the mirror.
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An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will beA. 36 cm away from the mirrorB. 30 cm away from the mirrorC. 30 cm towards the mirrorD. 36 cm towards the mirror
30 cm away from the mirror
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36 cm away from the mirror
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