# The focal length of a concave mirror is 80 cm. To obtain an inverted image two times the size of the object, the distance of the object from the pole

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The focal length of a concave mirror is 80 cm. To obtain an inverted image two times the size of the object, the distance of the object from the pole of mirror will be:
1. 90 cm
2. 100 cm
3. 110 cm
4. 120 cm

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Correct Answer - Option 4 : 120 cm

CONCEPT:

Mirror

• A mirror is a polished surface that reflects the light incident on it.
• Types of the mirror:
1. Plane mirror
2. Spherical mirror
• ​​Concave mirror
• Convex mirror

Mirror formula:

• The expression which shows the relation between object distance (u)image distance (v), and focal length (f) is called the mirror formula.

$⇒\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

Linear magnification (m):

• It is defined as the ratio of the height of the image (hi) to the height of the object (ho).

$⇒ m=\frac{h_{I}}{h_{O}}=-\frac{v}{u}$

CALCULATION:

Given f = -80 cm, and $\frac{h_{i}}{h_{o}}=-2$

Where hi = height of the image, and ho = height of the object

• The magnification of the mirror is given as,

$⇒ m=\frac{h_{I}}{h_{O}}=-\frac{v}{u}$

$⇒ v=-u×\frac{h_{i}}{h_{o}}$

$⇒ v=-u×\frac{(-2)}{1}$

⇒ v = 2u         -----(1)

According to the mirror formula,

$⇒ \frac{1}{f}=\frac{1}{u}+\frac{1}{v}$        -----(2)

Where u = distance of the object from the mirror, v = distance of the image from the mirror, and f = focal length

By equation 1 and equation 2,

$⇒ \frac{1}{f}=\frac{1}{u}+\frac{1}{2u}$

$⇒ \frac{1}{-80}=\frac{3}{2u}$

⇒ u = -120 cm

• Hence, option 4 is correct.