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Class X – Light : Reflection and Refraction (Part III – Lenses)
Refraction of Light by Spherical Lenses –
The working of a lens is based on the refraction of light rays when they through it.
A lens is a piece of transparent glass bound by two spherical surfaces. There are two types of
lenses : (1) Convex Lens, and (2) Concave Lens.
o A convex lens is thick at the centre but thinner at the edges.
o A concave lens is thin in the middle but thicker at the edges.
Optical Centre of Lens – The centre point of a lens is known as its optical centre. The optical
centre of a lens has a property that a ray of light passing through it does not suffer any
deviation and goes straight.
Principal Axis of Lens – A line passing through the optical centre of the lens and perpendicular
to both the faces of the lens is called principal axis of lens.
Principal Focus of Convex Lens – It is a point on its principal axis to which light rays parallel to
the principal axis converge after passing through the lens. A convex lens has two foci, one on
either side of the lens. The two foci are at equal distances from the optical centre.
A convex lens has real focus since all the light rays actually pass through the focus of a convex
lens.
The focal length of a lens is the distance between optical centre and principal focus of the lens.
A convex lens is also known as a converging lens because a parallel beam of light rays passing
through it converges to a point, called as focus or focal point.
A concave lens is called diverging lens because a parallel beam of light diverges after passing
through it.
Principal Focus of Concave Lens – It is a point on its principal axis from which light rays,
originally parallel to the axis, appear to diverge after passing through the concave lens.
A concave lens has virtual focus since the all the diverging rays only appear to originate from
the focus, whereas actually they are not.
Aperture of Spherical Lens – It is the surface from which the refraction of light takes place
through the lens. The aperture of spherical lens is represented by its diameter.
Rules for Obtaining Images Formed by Convex Lenses –
In general the image is formed at that point where at least two refracted rays meet or appear to meet.
Rule 1 – A ray of light which is parallel to the principal axis of convex lens, passes through its
focus after refraction through the lens.
Rule 2 – A ray of light after passing through the optical centre of a convex lens goes straight
after refraction through the lens.
Rule 3 – A ray of light passing through the focus of the convex lens becomes parallel to its
principal axis after refraction through the lens.
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Formation of Images by Convex Lens –
Case 1 – Object is placed between optical centre and focus – The image formed is :
o Behind the object (on the same side of the object but farther away from lens)
o Virtual and erect, and
o Larger in size than the object (magnified)
Case 2 – Object is placed at the focus of convex lens – The image formed is :
o At infinity
o Real and inverted, and
o Highly enlarged
Case 3 – Object is between focus and point at twice focal length – The image formed is :
o Beyond the point of twice focal length
o Real and inverted, and
o Larger than the object (magnified)
Case 4 – Object is at twice focal length (2f) – The image formed is :
o At a distance 2f on the other side of the lens
o Real and inverted
o Same size as the object
Case 5 – Object is beyond twice focal length (beyond 2f) – The image formed is :
o Between f and 2f on the other side of the lens
o Real and inverted, and
o Smaller than the object (diminished)
Case 6 – Object is at infinity – The image formed is :
o At the focus
o Real and inverted
o Much much smaller than the object (highly diminished)
Rules for Obtaining Images Formed by Concave Lenses –
Rule 1 – A ray of light which is parallel to the principal axis of concave lens, appears to be
coming from its focus after the refraction through the lens.
Rule 2 – A ray of light passing through the optical centre of a concave lens goes straight after
passing through the lens.
Rule 3 – A ray of light going towards the focus of a concave lens, becomes parallel to its principal
axis after refraction through lens.
Formation of images by Concave Lens –
No matter where the object is placed in front of a concave lens, it always forms a virtual, erect and
diminished image of the object.
Case 1 – Object anywhere between optical centre and infinity – The image formed is :
o Between optical centre and focus
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o Virtual and erect, and
o Diminished
Case 2 – Object is at infinity – The image formed is :
o At focus
o Virtual and erect, and
o Highly diminished
Sign Convention for Spherical Lenses –
According to the New Cartesian Sign Convention :
All the distances are measure from the optical centre of the lens.
The distances measured in the same direction as that of incident light are taken as positive.
The distances measured against the direction of incident light are taken as negative.
The distances measured upward and perpendicular to the principal axis are taken as positive.
The distances measured downward and perpendicular to the principal axis are taken as
negative.
The focal length of convex lens is considered as positive.
The focal length of concave lens is considered as negative.
Lens Formula –
A formula which gives the relationship between image distance (v), object distance (u), and focal length
(f) of a lens is known as lens formula, which is given as :
This lens formula applies to both types of spherical lenses, convex and concave.
Magnification Produced by Lenses –
The linear magnification (m) is the ration of the height of the image (h2) to the height of the object (h1) –
The linear magnification (m) produced by lens is alternatively given by the ratio of image distance (v) to
the object distance (u) –
With the proper sign of the v and u if –
Magnification m has positive value then the image is virtual and erect.
Magnification m has negative value then the image is real and inverted.
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Power of a lens –
Power of Lens (P) – It is a measure of degree of convergence or divergence of light rays falling
on it, and it is given by reciprocal of its focal length (f) in metres
A lens of short focal length has more power whereas a lens of long focal length has less power.
Dioptre – It is SI unit of power of a lens. It is indicated by D. One dioptre is the power of lens
whose focal length is 1 metre.
Power of convex lens is +ve.
Power of concave lens is –ve.
If a number of lenses are placed in close contact, then the power of the combination of lenses
is equal to the algebraic sum of the powers of individual lenses.
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