Question

Here's a Question from Science - Chapter: Light for Class 10 students.

4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of image and magnification. Describe what happens to the image as the needle is moved farther from the mirror.

Answer 1

Given that,

4. 5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm.

For a convex mirror, Focal length is positive. Image distance is positive, and Object distance is negative.

From the question,

Object distance ( u) = - 12 cm

Focal length ( f) = 15cm.

We know the Mirror formula,

$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

Now,

$\frac{1}{15} = \frac{1}{ - 12} + \frac{1}{v} \\ \\ \frac{1}{v} = \frac{1}{15} + \frac{1}{12} \\ \\ \frac{1}{v} = \frac{4 + 5}{60} \\ \\ \frac{1}{v} = \frac{9}{60} \\ \\ v = \frac{60}{9} = 20/3$

Therefore, Image distance is 6. 66 cm inside the mirror. The image will be virtual as well as diminished image..

Now,

Magnification = - v / u = - 20 / - 12 ( 3) = 20/36 = 10/18 = 5/9

We also know that,

Ratio of heights of image & object = m

In this case,

Height of image / Height of object = 1/2

Height of image = Height of object /2.

Next,

If the object ( needle) is taken far away from the mirror, What happens?

For a concave mirror, We know as the object moves from infinite to focus, Image size gradually increases. Let's see what happens in case, of convex mirror.

Consider, i have taken the object to 30cm away,

From the mirror formula,

1/15 + 1/30 = 1/v

3/30 = 1/v

v = 10cm.

m = - 10/ - 30 = 1/3.

Magnification decreased, So as the needle is taken away from the mirror, image size decreases.

Answer 2

Answer:-

Given;

Focal Length = 15cm.

Height of Object = 4.5cm.

Object's Distance = -12 cm.

By Using Mirror Formula,

1/f = 1/u + 1/v

=> 1/15 = 1/(-12) +1/v

=> 1/15 + 1/12 = 1/v

=> (4+5)/60 = 1/v

=> v = 60/9

=> v = 20/3.

Now,

By Using Formula of Magnification ,

m = -v/u = hi / ho

Where ,

hi = Height of Image.

& Ho = Height of Object.

=> hi = ( -v × ho)/ u

=> hi = ( - 20/3 × 4.5) / -12

=> hi = (20 × 4.5 ) / ( 12 × 3)

On Solving this we get,

hi = 2.5 cm.

Hence,

The Height of Image is 2.5cm.

Therefore,

Magnification = hi / ho

=> M = 2.5 / 4.5 = 0.56

Hence,

Magnification is 0.56.

If the Needle is moved towards the mirror the Image will become Smaller & If it will move away from the mirror the image will become Larger.