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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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Text Solution
Solution : Givenn u=40 cm (negative) <br> `m=1/4` (negative for the real image) <br> a. From `m=-v/u,-1/4=-v/((-40))` or v=-10 cm <br> Thus the image is formed at a distance 10 cm in front of the mirror. <br> b. Now from relation `1/u+1/v=1/f` <br> `1/f=1/((-40))+1/((-10))` <br> `=(-5)/40` <br> or `f=(-40)/5=-8cm` <br> i.e., the focal length of concave mirror is 8cm.