Question

If a man’s face is 25 cm in front of concave shaving mirror producing erect image 1.5 times the size of face, focal length of the mirror would be
(a) 75 cm
(b) 25 cm
(c) 15 cm
(d) 60 cm

Answer 1

hey user

Explanation:

Given :

Object distance u= -25cm

m=1.4

m= -v/u

v= mx -u = 1.4 x 25 = 14x25/10 = 35 cm

From mirror equation :

1/f=1/v+1/u

1/f= 1/35 -1/25

= 5-7/135 = - 2/ 135

f= - 87.5cm

So focal length of concave mirror is 87. 5cm

Answer 2

Answer:

Focal length of the concave mirror will be 15 cm

Explanation:

Let us assume that the object height $(ho)$ is $x$

As per the given information, image height $(hi)$ will be $1.5x$

image distance $(di)$ is 25 cm.

Magnification equation states that, $M=\frac{hi}{ho}=\frac{di}{do}$

where, $do$ is the object distance.

Applying the equation to the given data, we get

$M=\frac{1.5x}{x}=\frac{di}{do}$

Hence, $di=1.5do$

Now, the mirror equation states that $\frac{1}{f}= \frac{1}{do}+\frac{1}{di}$

where $f$ is focal length of concave lens.

Applying the equation to the given data, we get

$\frac{1}{f}= \frac{1}{do}+\frac{1}{1.5do}$

∴ $\frac{1}{f}=\frac{2.5}{1.5do}$

Now $do$ given is 25 cm,

Hence, $\frac{1}{f}=\frac{2.5}{1.5X25}$

∴ $f= \frac{37.5}{2.5}$

  $f=$ 15 cm