The correct answer is option 4 i.e At the focal point
If an object is at infinity, the position of an image formed due to the convex lens is at the focal point.
Convex lens converge parallel rays coming from object at infinity and a highly diminished - point sized, real and inverted image is formed at principal focus.
Properties of the image formed
The image formed is highly diminished, real and inverted.
There are two types of lenses -
Convex Lens: This type of lens is also known as Converging lens as when light passes through it converges at one point.
Concave Lens: This type of lens is also known as Diverging lens as all the rays diverged when light passes through it.
Find the focal length (in cm) of a convex lens if object is placed at 10 cm from the lens and image is obtained at 50 cm from the lens on the same side?
Where f is the focal length of the lens, v is the distance of the image on the principal axis from the optical centre. u is the distance of the object on the principle axis from the optical centre.
Sign convention: In the convex lens
The distance measured from the optical centre (o) to the left side is taken as negative.
The distance measured from the optical centre (o) to the right side is taken as positive.
The distance measured from the principal axis (o) to downward be taken as negative.
The distance measured from the principal axis (o) to upward be taken as positive.
Explanation:
The lens formula can be given by the following relation.
\(\frac{1}{{\bf{f}}} = \frac{1}{{\bf{v}}} - \frac{1}{{\bf{u}}}\) or
\(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\)
Additional Information
Lens Maker's Formula:
If R1 and R2are the radii of curvature of first and second refracting surfaces of a thin lens of focal length f and refractive index μ (w.r.t. surrounding medium) then the relation between f, μ, R1 and R2 are known as lens maker’s formula.
Lens: The transparent curved surface which is used to refract the light and make an image of any object placed in front of it is called a lens.
The lens whose refracting surface is upside is called a convex lens.
The convex lens is also called a converging lens.
Lens formula is given by:
\(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\)
The magnification of the lens is given by:
Magnification (m) = v/u
Where u is object distance, v is image distance and f is the focal length of the lens
CALCULATION:
A lens formula may be defined as the formula which gives the relationship between the distance of image (v), the distance of the object (u), and the focal length (f) of the lens.
Where f is the focal length, n is the refractive index of the material used, R1 is the radius of curvature of sphere 1 and R2 is the radius of curvature of sphere 2.
The power of a lens is defined as the reciprocal of its focal length in meters, or D = 1/f,
Where D is the power in diopters and f is the focal length in meters.
Calculation:
Given μ = 1.5, R1 = ∞ and R2 = −20cm (the object lies on the plane side)
A parallel beam of light is incident on a glass item behind curtain ABCD. The emergent rays coming out from the item are as given in the following figure. Which item could be behind the curtain?
Where, f is the focal length (half the radius of curvature), n_{21} is the refractive index of the material used, R1 is the radius of curvature of sphere 1 and R2 is the radius of curvature of sphere 2
Lens formula is given by:
\(\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\)
Where u is object distance, v is image distance and f is the focal length of the lens
The transparent curved surface which is used to refract the light and make an image of any object placed in front of it is called a lens.
The lens whose refracting surface is upside is called a convex lens and the lens whose refracting surface is inside is called a concave lens or diverging lens.
Concave lenses diverge light rays and hence are also called diverging lenses.
Positions of the object and image:
Position of the object
Position of the image
The relative size of the image
Nature of the image
1. At infinity
At focus F_{1}
Highly diminished, point-sized
Virtual and erect
2. Between infinity and optical center O of the lens
Between focus F_{1} and optical center O
Diminished
Virtual and erect
EXPLANATION:
When the object is between the infinity and optical center of the lens then the image forms between focus and optical center which is diminished, virtual and erect. So option 1 is correct.
Lens: The transparent curved surface which is used to refract the light and make an image of any object placed in front of it is called a lens.
Convex lens: A lens having two spherical surfaces, bulging outwards is called a double convex lens (or simply convex lens).
It is thicker in the middle as compared to the edges.
Convex lenses converge light rays and hence, convex lenses are also called converging lenses.
EXPLANATION:
To obtain an enlarged real inverted image beyond 2F_{2} after refraction by a convex lens, the object should be placed between F_{1} and 2F_{1}. So option 2 is correct.
EXTRA POINTS:
Nature, position, and relative size of the image formed by a convex lens for various positions of the object:-
Position of the object
Position of the image
The relative size of the image
Nature of the image
At infinity
At focus F_{2}
Highly diminished, point-sized
Real and inverted
Beyond 2F_{1}
Between F_{2} and 2F_{2}
Diminished
Real and inverted
At 2F_{1}
At 2F_{2}
Same size
Real and inverted
Between F_{1} and 2F_{1}
Beyond 2F_{2}
Enlarged
Real and inverted
At focus F_{1}
At infinity
Infinitely large or highly enlarged
Real and inverted
Between focus F_{1 }and optical center O
On the same side of the lens as the object
Enlarged
Virtual and erect
NOTE:
2F_{1} is centre of curvature (C) on the left side of the lens and 2F_{2} is centre of curvature (C) on the right side of the lens.
Focus: When the parallel beam of rays of light coming from different directions meets at a point is known as Focus.
EXPLANATION:
Convergent Ray: When light rays coming from different direction meet at a point then such rays is known as convergent rays.
When parallel beams of sunlight are made to the incident so that the rays converge at the focus point.
Focus is the point where the parallel beam of light rays originating from a point on the object converges.
Additional Information
Center of curvature: It is the center of the sphere from which the mirror is cut, or we can say the center of the sphere is called the center of curvature as shown in the diagram
It is represented by C
Pole: The midpoint of the aperture of the mirror is known as Pole.
A thin-walled cylindrical pressure vessel having a radius of 0.6 m and wall thickness of 24 mm is subjected to an internal pressure of 1000 kP. The hoop stress (MPa) developed is
In optical systems composed of lenses, the position, magnitude and errors of the image depend upon the refractive indices of the glass.
Chromatic aberration: The defect of a lens whereby rays of white light proceeding from a point get dispersed into their components and conveyed to various foci, forming a blurred and coloured image is known as Chromatic aberration.
If white light is employed, all the images are formed and they cause confusion, named chromatic aberration. The absence of this error is termed achromatism, and an optical system so corrected is termed achromatic.
Spherical aberration is a type of aberration found in optical systems that use elements with spherical surfaces. Lenses and curved mirrors are most often made with surfaces that are spherical, because this shape is easier to form than non-spherical curved surfaces. To avoid spherical aberration Aplanatic lens (zero spherical aberration) are used.
In simple words, Chromatic aberration is related to overlap of different images and Spherical aberration is related to poor focussing.
Explanation:
If two or more lenses are combined together in such a way that this combination produces images of different colours at the same point and of the same size, then this property is called ''achromatism''. Concave and convex type of lenses are used for this combination.
This proper combination of a convex and a concave lens may result in no change in focal length of the lens system for different lights. So, in this combination image is unaffected by variation of refractive index with wavelength.
An achromatic combination of lenses provide deviation without dispersion. So, images are unaffected by variation of refractive index with wavelength.
The chromatic aberration of one lens is balanced by other lenses. Due to this, the white light do no undergo dispersion.
So, Images unaffected by variation of a refractive index with wavelength