Question

A 2 cm wide object is placed 3 cm in front of a 1 cm focal length concave mirror. The final image will be: a) one third as wide and inverted. b) same size and erect. c) half as wide and inverted. d) three times bigger and inverted. e) five times bigger and erect.

Answer 1

Answer: The correct answer is Option c.

Step-by-step explanation:

For concave mirror, sign convention used is:

f = +ve

u = +ve (object is in front of mirror)

• To calculate the distance of image from the image, we use the mirror formula:

`(1)/(u)+(1)/(v)=(1)/(f)`

where,

u = distance of object from mirror = +3 cm

v = distance of image from mirror = ?

f = focal length of the mirror = +1 cm

Putting values in above equation, we get:

`(1)/((+3))+(1)/(v)=(1)/(1)\\\\v=(2)/(3)cm`

As, the image distance is coming out to be positive, this means that image is real.

• To calculate the magnification of image, we use the equation:

`m=-(v)/(u)`

We are given:

`u=3cm\\v=(2)/(3)cm`

Putting values in above equation, we get:

`m=-((2)/(3))/(3)\\\\m=(-1)/(2)`

As, the magnification is coming out to be negative, this means that image is inverted with respect to object. Also, the image is reduced in size.

Hence, the correct answer is Option c.