Question

Determine the image distance for a 10.00-cm tall object placed 15.0 cm from a concave mirror having a focal length of 5.0 cm.

Answer 1

As the mirror is concave, so the focal length is negative.
u = -15cm
f = -5cm
By using mirror formula:
1/v = 1/f - 1/u
substitute the given values:
1/v = 1/-5 - (1/-15)
= -3+1/15
= -2/15
v = -15/2cm
v = -7.5cm

Answer 2

Given :

⇒ $H_o$  = 10 cm {Height of Object}

⇒ $D_o$ = -15 cm {Distance of Object}

⇒ f = -5 cm {Focal Length.}

We used - because It's concave mirror

To Find out :

⇒ $D_i$ = ?

Formula to be used here :

⇒ $\frac{1}{f} = \frac{1}{D_o} + \frac{1}{D_i}$

Finding out value of $D_i$ by putting values in above formula :

⇒ $\frac{1}{f} = \frac{1}{D_o} + \frac{1}{D_i}$

⇒ $\frac{1}{5} = \frac{1}{15} + \frac{1}{D_i}$

⇒ $\frac{1}{-5} - \frac{1}{-15} = \frac{1}{D_i}$

⇒ $\frac{-1\times3}{5\times3} - \frac{1}{-15} = \frac{1}{D_i}$ {LCM}

⇒ $\frac{-3}{15} - \frac{1}{-15} = \frac{1}{D_i}$

⇒ $\frac{-3+1}{15} = \frac{1}{D_i}$

⇒ $\frac{-2}{15} = \frac{1}{D_i}$

⇒ $D_i$ = $\frac{15}{-2}$

⇒ $D_i$ = -7.5 cm

∴ Image distance = -7.5 cm

Thanks!