Question

An object when placed in front of convex lens forms a real image of 0.5 magnification. If the distance of the image from the lens is 24 cm, Calculate Focal Length of Lens.​

Answer 1

`\text{u =?} \\ \text{ v = 24cm} \\ \text{ m = 0.5} \\ \text{ f = ?}`

`\implies \text{m} = \frac{ \text{v}}{ \text{u}} = \frac{24}{ \text{u}}`

`\implies 0.5 = (1)/(2) = \frac{24}{ \text{u}} \\ \\ \therefore \text{u} = 48 \text{cm}`

`\implies \frac{1}{ \text{f}} = \frac{1}{ \text{v}} - \frac{1}{ \text{u}}`

`\implies \text{f} = (1)/(24) - (1)/(48) = (2 - 1)/(48) = (1)/(48)`

`\text{f} = 48 \text{cm}`

`\underline{ \text {According To Question,}}`

`\text{24cm is the distance of object from lens,}`

`\text{m} = \frac{ \text{v}}{ \text{u}} \\ \\ \implies (1)/(2) = \frac{ \text{u}}{24}`

`\therefore \text{v} = (24)/(2) = 12 \text{cm}`

`\implies \frac{1}{ \text{f}} = \frac{1}{ \text{v}} - \frac{1}{ \text{u}}`

`\implies \frac{1}{ \text{f}} = (1)/(12) - ( (1)/( - 24) )`

`\implies \frac{1}{ \text{f}} = (1)/(12) + (1)/(24) = (2 + 1)/(24) = (3)/(24)`

`\implies \text{f} = (24)/(3) = 8 \text{cm}`

Hope this helps