Question

An object of height 4.25 mm is placed at a distance of 10 cm from a convex lens of power +5D. Find (i) focal length of the lens, and (ii) size of the image.

Answer 1

Answer:

Here is your answer.

Sorry for so much cutting

Answer 2

The focal length of the lens is 20 cm and the size of image is 8.50 mm.

Explanation:

Object height h = 4.25 mm = 42.5 cm (1 cm = 10 mm)

Object distance u = -10 cm

Power, p = + 5D

Using Power, formula, focal length can be calculated

$(i) P=\frac{1}{f}$

$f=\frac{1}{p}=\frac{1}{5}=0.2 m=20 \mathrm{cm}$

Using the lens formula, we get:

$\text { (ii) } \frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

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

$=\frac{1}{20}+\frac{1}{-10}$

$=\frac{-1}{20}$

$V=-20$

$m=\frac{h^{\prime}}{h}=\frac{v}{u}$

$\Rightarrow \frac{h^{\prime}}{h}=\frac{-20}{-10}$

$\Rightarrow \frac{h^{\prime}}{h}=\frac{-20}{-10}$

$\Rightarrow \frac{h^{\prime}}{42.5}=\frac{-20}{-10}$

$h^{\prime}=85 \mathrm{cm}=8.5 \mathrm{mm}$

Therefore, the image is 8.5mm long.