Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# A convex lens of focal length $1.0\,m$ and a concave lens of focal length $0.25\,m$ are $0.75\,m$ apart. A parallel beam of light is incident in the convex lens. The beam emerging after refraction from both lenses is:A. Parallel to the principal axisB. ConvergentC. DivergentD. None of the above

Last updated date: 15th Aug 2024
Total views: 341.7k
Views today: 9.41k
Verified
341.7k+ views
Hint: A lens is a piece of transparent glass which is bounded by two surfaces out of which at least one surface is spherical. Refraction is the bending of light when it obliquely travels from one medium to another medium. Here the power of combination of lenses is applied.

From the question, convex lenses and concave lenses are $0.75{\text{ m}}$ apart.
Therefore, from the power of combination of lenses.
$\dfrac{1}{f} = \dfrac{1}{{{f_1}}} + \dfrac{1}{{{f_2}}} - \dfrac{d}{{{f_1}{f_2}}}$
Were, ${f_1}$ is the focal length of convex lens $= 1{\text{ m}}$
${f_2}$ is the focal length of concave lens $= 0.25{\text{ m}}$
$d$ is the distance between the lenses $= 0.75{\text{ m}}$
$\dfrac{1}{f} = \dfrac{1}{{ + 1}} + \dfrac{1}{{ - 0.25}} - \dfrac{{0.75}}{{1 \times \left( { - 0.25} \right)}}$
$\Rightarrow \dfrac{1}{f} = 1 - 4 + 3$
Further simplifying we get,
$\Rightarrow \dfrac{1}{f} = 4 - 4$
$\therefore \dfrac{1}{f} = 0$
Therefore, the focal length will be infinity and the power will become zero. As the power is zero therefore if the incident beam of light is parallel then the emerging beam of light will be also parallel.

Therefore, the correct answer is option A.

Power of a lens: The power of a lens is defined as the reciprocal of its focal length. It is represented by the letter $P$. The power $P$ of a lens of focal length $f$ is given by,
$P = \dfrac{1}{f}$
The SI unit of power is diopter when focal length is in meters. It is noted by $D$. Hence one diopter is a power of lens whose focal length is 1 metre.