Question

The focal length of a concave lens is 40cm. Where should an object be placed infront of it to get its half- sized image?​

Answer 1

Explanation:

object should be placed at a distance of 40 cm in front of a concav lens so that will get as a half of the size of object

Answer 2

➠ Questíon :-

↬ The focal length of a concave lens is 40cm. Where should an object be placed infront of it to get its half- sized image?

➠ Gíven :-

↬ Focal length,f = - 40cm

(negative because it is concave mirror)

➠ To fínd :-

↬ Where should an object be placed infront of it to get its half- sized image

➠ Solutíon :-

we know,

• hi = image height
• ho = object height
• u = object distance
• v = image distance

$\longrightarrow \mathrm{ hi = ho \times \frac{1}{2} = \frac{ho}{2}}$

$\longrightarrow \rm m = \frac{hi}{ho} = \frac{1}{2}$

$\longrightarrow \rm so \: \frac{v}{u} = \frac{1}{2}$

$\longrightarrow \boxed{ \rm \: 2v = u}........ \: \: 1$

now ,using lens formula

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

$\longrightarrow \tt \frac{ \: 1}{ - 40} = \frac{1}{v} - \frac{1}{2v} \: \: \: \: (2v = u)$

$\longrightarrow \tt \frac{ - 1 \: \: }{40} = \frac{2 - 1}{2v}$

$\longrightarrow \tt \cancel\frac{ - 2 \: \: }{40} = \frac{1}{v}$

$\longrightarrow \tt \frac{ - 1 \: \: }{20} = \frac{1}{v}$

$\longrightarrow \boxed {\tt v = - 20cm}$

using equation (1)

$\longrightarrow \tt u = 2v$

$\longrightarrow \tt u = 2( - 20)$

$\longrightarrow \boxed{ \tt u = - 40cm}$

Hence, the object should we placed at a distance of 40cm in front of concave lens

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know more.....

• Both converge parallel rays to a focal point, have positive focal lengths, and form images with similar characteristics.
• A concave lens acts a lot like a convex mirror. Both diverge parallel rays away from a focal point, have negative focal lengths, and form only virtual, smaller images.
• A highly diminished point sized, virtual and erect image is formed when object is at infinity by a concave lens at principal focus F1. Properties of Image: Image is point sized, highly diminished, virtual and erect.