Question

a convex lens of focal length 15 cm forms an image at 10 cm from the lens how far the object is placed from lens and draw a ray diagram. find the power of lens

Answer 1

Step 1: Given that:

Focal length of the convex lens($f$) = $+15cm$

Image distance($v$) = $-10cm$

(Note:

1. The distances taken left to the optical centre of the lens are taken as negative.
2. ​The distances taken right to the optical centre of a lens are taken as positive.
3. Thus, the object distance is always negative.
4. And the focal length of the convex lens is positive.)

Step 2: Formula used:

Lens formula is given by:

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

Where u is the object distance, v is image distance and f is the fiscal length of the lens.

The power of the lens is given by;

$P=\frac{1}{f\left(inmetre\right)}$

Step 3: Calculation of object distance:

$\frac{1}{-10cm}-\frac{1}{u}=\frac{1}{+15cm}$

$-\frac{1}{10}-\frac{1}{u}=\frac{1}{15}$

$-\frac{1}{u}=\frac{1}{15}+\frac{1}{10}$

$-\frac{1}{u}=\frac{2+3}{30}$

$-\frac{1}{u}=\frac{5}{30}$

$-\frac{1}{u}=\frac{1}{6}$

$u=-6cm$

Step 4: Calculation of power of the lens:

$P=\frac{1}{\frac{15}{100}m}$

$P=\frac{100}{15}$

$P=\frac{20}{3}$

$P=+6.67D$

Thus,

Object distance= $6cm$

Power of the lens= $+6.67D$