Question:
A point object is placed at a distance of 20 cm from a thin planoconvex lens of focal length 15 cm. The plane surface of the lens is now silvered. The image created by the system is at
A point object is placed at a distance of 20 cm from a thin planoconvex lens of focal length 15 cm. The plane surface of the lens is now silvered. The image created by the system is at
Updated On: Oct 14, 2023
- 60 cm to the left of the system
- 60 cm to the right of the system
- 12 cm to the left of the system
- 12 cm to the right of the system
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The Correct Option is C
Solution and Explanation
Focal length for the lens is given by,
$f =\frac{ R }{\mu-1}=15$
After silvering the plane surface of the lens it converts to the thin plano convex mirror. focal length is now change. $\therefore$ For mirror focal length $f ^{\prime}$ is given by, $f ^{\prime}=\frac{ R }{2(\mu-1)}=7.5$
Thus, for the mirror eq is, $\frac{1}{ v }+\frac{1}{ u }=\frac{1}{ f ^{\prime}}$
Where $u =$ distance of the object from the mirror $=-20$,
and $v =$ distance of the image from the mirror
Thus, substituting the values of $f ^{\prime}=7.5$ and $u =-20$
$\frac{1}{ v }+\frac{1}{-20}=\frac{1}{7.5}$
$\therefore v =-12 cm$ minus sign indicates that it is to the left of the system.
$f =\frac{ R }{\mu-1}=15$
After silvering the plane surface of the lens it converts to the thin plano convex mirror. focal length is now change. $\therefore$ For mirror focal length $f ^{\prime}$ is given by, $f ^{\prime}=\frac{ R }{2(\mu-1)}=7.5$
Thus, for the mirror eq is, $\frac{1}{ v }+\frac{1}{ u }=\frac{1}{ f ^{\prime}}$
Where $u =$ distance of the object from the mirror $=-20$,
and $v =$ distance of the image from the mirror
Thus, substituting the values of $f ^{\prime}=7.5$ and $u =-20$
$\frac{1}{ v }+\frac{1}{-20}=\frac{1}{7.5}$
$\therefore v =-12 cm$ minus sign indicates that it is to the left of the system.
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Concepts Used:
Spherical Lenses
Lenses that are made by combining two spherical transparent surfaces are called spherical lenses. In general, there are two kinds of spherical lenses. Lenses that are made by joining two spherical surfaces that bulge outward are convex lenses, whereas lenses that are made by joining two spherical surfaces that curve inward are concave lenses.
Properties of Convex lens:
- In this, the lenses are thicker in the middle and thinner at the edges.
- They have a positive focal length.
- It intersects the incident rays towards the principal axis
- These lenses are used in the camera, focus sunlight, projector microscope, simple telescope, overhead projector, magnifying glasses, etc.
Properties of Concave lens:
- These lenses are thinner in the middle and thicker at the edges.
- They have a negative focal length.
- It parts the incident rays away from the principal axis.
- These are used in the glasses, spy holes, some telescopes in the doors, etc.