A lens forms a virtual, diminished image of an object placed at 2 m from it. The size of image is half of the object. Which one of the following statements is correct regarding the nature and focal length of the lens?

Question

A lens forms a virtual, diminished image of an object placed at 2 m from it. The size of image is half of the object. Which one of the following statements is correct regarding the nature and focal length of the lens? (A) Concave, |f|=1 m (B) Convex, |f|=1 m (C) Concave, |f|=2 m (D) Convex, |f|=2 m

Tardigrade Admin · Accepted Answer

m=(f/f+u), (1/2)=(f/f-2) ; or 2 f=f-2 or f=-2 m |f|=2 metre. Since the image is virtual as well as diminished, therefore the lens is concave.

Q. A lens forms a virtual, diminished image of an object placed at $2 m$ from it. The size of image is half of the object. Which one of the following statements is correct regarding the nature and focal length of the lens?

Concave, $∣ f ∣ = 1 m$

Convex, $∣ f ∣ = 1 m$

Concave, $∣ f ∣ = 2 m$

Convex, $∣ f ∣ = 2 m$

$m = \frac{f}{f + u}, \frac{1}{2} = \frac{f}{f - 2}$ ;
or $2 f = f - 2$ or $f = - 2 m$
$∣ f ∣ = 2$ metre. Since the image is virtual as well as diminished,
therefore the lens is concave.

Q. A lens forms a virtual, diminished image of an object placed at 2m from it. The size of image is half of the object. Which one of the following statements is correct regarding the nature and focal length of the lens?

Concave, ∣f∣=1m

Convex, ∣f∣=1m

Concave, ∣f∣=2m

Convex, ∣f∣=2m