Name: Power of Lenses
Uploaded: 2019-07-19
Duration: 4 min 48 s
Description: What is the difference between different eyeglasses? The power of a lens is the measure of how well the lens converges or diverges light rays. Let’s visualise.

Question

A candle of

2 cm

height is placed at a distance of

15 cm

in front of a convex lens of focal length

10 cm

. Draw diagram to find the position and size of image.

Accepted Answer

Given,

Focal length of the convex lens. $f = 10 cm$ ,

The height of the object, $h_{o} = 2 cm$ ,

Object distance, $u = - 15 cm$ ,

Let $v$ and $h_{i}$ be image distance and image height respectively.

According to Lens formula,

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ ,

$\frac{1}{(10)} = \frac{1}{v} - \frac{1}{(- 15)}$ ,

$\frac{1}{v} = \frac{3 - 2}{30} = \frac{1}{30}$ ,

$v = 30 cm$

Therefore, the image will be formed at a distance of $30 cm$ behind the lens.

We know that the magnification of the lens,
$m = \frac{v}{u} m = \frac{30}{- 15} = - 2$

Also, size/height of the image, $h_{i} = m \times h_{o} = 2 \times - 2 = - 4 cm$

The size of the image formed will be $4 cm$ . Since the magnitude of magnification is greater than one, the image formed will be magnified. Also, the negative sign of the magnification indicates that the image is inverted and hence real.

The image formation can be represented as below.

Where,

$O B = u = 15 cm$

$O B' = v = 30 cm$

$A B = h_{i} = 2 cm$

$A' B' = h_{i} = 4 cm$

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