Question

Rohit placed a pencil perpendicular to principal axis in front of a converging

mirror of focal length 30 cm. The image formed is twice the size of the pencil.
Calculate the distance of the object from the mirror.

Answer 1

Using the mirror equation and magnification formula, the object distance is calculated to be 60 cm from the mirror when the image is twice the size of the object using a converging mirror with a focal length of 30 cm.

Step-by-step explanation:

To calculate the distance of the object (pencil) from the mirror when an image is formed that is twice the size of the object using a converging mirror (concave mirror), we use the mirror equation and magnification formula. The mirror equation is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. The magnification formula is m = -di/do, where m is the magnification.

Given that the image is twice the size of the object, the magnification m is -2 (it is negative because the image by a converging mirror is inverted). Hence, with the focal length f being -30 cm (negative because the mirror is concave), we must solve the following equations simultaneously:

1. m = -2 = -di/do
2. 1/f = 1/do + 1/di

Using the second equation with the known f, we get 1/-30 = 1/do + 1/di. To find do, we can substitute di using di = -2do from the magnification equation into the mirror equation. The two equations become:

1. 1/-30 = 1/do - 1/(2do)
2. 1/-30 = (2do - do)/(2do^2)
3. 1/-30 = 1/(2do)
4. do = 2(-30)
5. do = -60 cm

The negative sign indicates that the object is placed in front of the mirror. Therefore, the object distance do is 60 cm from the mirror.

Answer 2

45 cm ( in my opinion)‍♀️

Step-by-step explanation:

( Using the mirror formula)

1/ u + 1/v = 1/f

( introducing magnification; m into the formula )

u( 1/u + 1/v ) =u×1/f

1 + u/v =u/f

( But u/v =1 ÷v/u= 1/m)

1 +1/m =u/f

(Supposing m is actually equal to 2, and f =30 cm, then;)

1 + 1/2 =u/30

2+1= u/15

3=u/15

3×15=u

45 cm=u