Question 218: Ray Optics

Question

An upright object is placed at a distance of
40 cm in front of a convergent lens of focal
length 20 cm. A convergent mirror of focal
length 10 cm is placed at a distance of 60 cm
on the other side of the lens. The position and
size of the final image will be :

Accepted Answer

In given system of lens and mirror, position of object O in front of lens is at a distance 2f. i.e. u = 2f = 40 cm
So, image (I
1
) formed is real, inverted and at a distance, v = 2f = 2 $$	imes$$ 20 = 40 cm, (behind lens) magnification, $${m_1} = {v \over u} = {{40} \over {40}} = 1$$
Thus, size of image is same as that of that of object. This image (I
1
) acts like a real object for mirror.
As object distance for mirror is
u = C = 2f = $$-$$ 20 cm
where, C = centre of curvature.
So, image (I
2
) formed by mirror is at 2f.
$$	herefore$$ For mirror v = 2f = 2($$-$$ 10) = $$-$$ 20 cm
Magnification, $${m_2} =  - {v \over u} =  - {{( - 20)} \over {( - 20)}} =  - 1$$
Thus, image size is same as that of object.
The image I
2
formed by the mirror will act like an object for lens.
As the object is at 2f distance from lens, so image (I
3
) will be formed at a distance 2f or 40 cm. Thus, magnification,
$${m_3} = {v \over u} = {{40} \over {40}} = 1$$
So, final magnification, $$m = {m_1} 	imes {m_2} 	imes {m_3} =  - 1$$
Hence, final image (I
3
) is real, inverted of same size as that of object and coinciding with object.

Answer

20 cm from the convergent mirror, same
size as the object

Answer

40 cm from the convergent mirror, same
size as the object

Answer

40 cm from the convergent lens, same
size as the object

Answer

20 cm from the convergent mirror, twice the
size of the object

Ray Optics

An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be :

Choose the correct answer: