Question

A dentist uses a mirror in front of a decayed tooth at a distance of 4 cm from the tooth to get a four times magnified image in the mirror. Use mirror formula to find the focal length and nature of the mirror used.

Answer 1

Given :-

▪ A dentist uses a mirror in front of a decayed tooth at a distance of 4 cm from the tooth. Doing so he gets an image which is 4 times the object size.

To Find :-

▪ Focal length and nature of the mirror used.

Solution :-

It is given that the image is magnified 4 times. So, Using the magnification formula,

⇒ m = -v / u = (height of image)/(height of object)

⇒ -v/u = 4/1

⇒ v = - 4u ...(1)

Now, Using the mirror formula, focal length can be calculated as,

⇒ 1/f = 1/v + 1/u

⇒ 1/f = -1/4u + 1/u [ from (1) ]

⇒ 1/f = (4 - 1)/4u

⇒ 1/f = 3/4u

⇒ 1/f = 3/4×-4

⇒ f = -16/3 = -5.33 cm

Since the focal length is negative hence the given mirror is Concave mirror.

Also, The image formed would be virtual because the object distance is less than the focal length (Excluding the negative sign).

So,

• Focal length = -5.33 cm
• Mirror used = Concave mirror