Question

A real image 1/5 the the size of objectis formuedat a distance of 18cm from a mirror what is the nature mirror calculate its focal length

Answer 1

Solution :-

As per the given question ,

• Object distance (u) = - 18 cm ( distances are always measured from the pole of the mirror )

• hi = - ho / 5 ( real ,inverted )

Magnification is given by the formula ,

➝ m = - v / u = hi / ho

here,

• v = image distance
• u = object distance

• hi = height of the image
• ho = height of the object

➝ - v = hi x u / ho

➝ - v = - ho x u / 5 ho

➝ v = u / 5

As per mirror formula ,

➝ 1 / f = 1 / v + 1 / u

here ,

• f = focal length
• v = image distance
• u = object distance

Now , let's substitute the value of v in the above equation ,

➝ 1 / f = 5 / u + 1 / u

➝ 1 / f = 6 / u

➝ f = u / 6

➝ f = 18 / 6

➝ f = 3 cm

The focal length of the mirror is 3 cm .

It is a convex mirror as the focal length is positive