Definition
Terms related to lenses
Centre of curvature (C): The centre of sphere of which lens is a part.
Radius of curvature (R): The radius of sphere of which lens is a part.
Principal axis: Line joining the centre of curvatures of two lenses.
Optical centre (O): The point on the principal axis of a thin lens through which a ray of light passes undeviated.
First focal point (): It is a point on the principal axis of the lens such that the rays of light starting from it (convex lens) or appearing to meet at the point (concave lens) after refraction from the two surfaces of the lens become parallel to the principal axis of the lens.
Second focal point (): It is a point on the principal axis of the lens such that the rays of light parallel to the principal axis of the lens after refraction from both the surfaces of the lens pass through this point (convex lens) or appear to be coming from this point.
Focal plane: Plane passing through focus and perpendicular to the principal axis.
Radius of curvature (R): The radius of sphere of which lens is a part.
Principal axis: Line joining the centre of curvatures of two lenses.
Optical centre (O): The point on the principal axis of a thin lens through which a ray of light passes undeviated.
First focal point (): It is a point on the principal axis of the lens such that the rays of light starting from it (convex lens) or appearing to meet at the point (concave lens) after refraction from the two surfaces of the lens become parallel to the principal axis of the lens.
Second focal point (): It is a point on the principal axis of the lens such that the rays of light parallel to the principal axis of the lens after refraction from both the surfaces of the lens pass through this point (convex lens) or appear to be coming from this point.
Focal plane: Plane passing through focus and perpendicular to the principal axis.
Formula
Calculate focal length of convex lens by plane mirror
Experiment:
To find the focal length of a convex lens by the plane mirror method.
Procedure:
1. Arrange the plane mirror, convex lens and object as shown in the figure.
2. Fix the position of the plane mirror at one end of the optical bench. Now put the convex lens at x distance from the plane mirror and locate the position of image behind the convex lens in a way to have no parallax between the image and object.
3. Record the position of the plane mirror, convex lens and the object.
4. The distance between the convex lens and object pin is the focal length of the convex lens.
To find the focal length of a convex lens by the plane mirror method.
Procedure:
1. Arrange the plane mirror, convex lens and object as shown in the figure.
2. Fix the position of the plane mirror at one end of the optical bench. Now put the convex lens at x distance from the plane mirror and locate the position of image behind the convex lens in a way to have no parallax between the image and object.
3. Record the position of the plane mirror, convex lens and the object.
4. The distance between the convex lens and object pin is the focal length of the convex lens.
Example
Focal length of convex lens by plane mirror
Problem:
A convex lens of focal length 15 cm is placed
infront of a plane mirror at a distance 25 cm from the mirror. Where on the optical axis and from the centre of the lens should a small object be placed such that the final image coincides with the object?Solution:
The focal length of the lens is 15 cm. If the object is placed at 15 cm from lens, light rays after coming from lens will be parallel to axis and after reflection from plane mirror it will retrace its path and form the image at very same position as the object as shown in the image.
A convex lens of focal length 15 cm is placed
infront of a plane mirror at a distance 25 cm from the mirror. Where on the optical axis and from the centre of the lens should a small object be placed such that the final image coincides with the object?Solution:
The focal length of the lens is 15 cm. If the object is placed at 15 cm from lens, light rays after coming from lens will be parallel to axis and after reflection from plane mirror it will retrace its path and form the image at very same position as the object as shown in the image.
Definition
Sign convention
Sign convention is a set of rules to set signs for image distance, object distance, focal length, etc for mathematical analysis of image formation. According to it:
Convex lens has positive focal length and concave lens has negative focal length.
- Object is always placed to the left of lens.
- All distances are measured from the optical centre of the mirror.
- Distances measured in the direction of the incident ray are positive and the distances measured in the direction opposite to that of the incident rays are negative.
- Distances measured along y-axis above the principal axis are positive and that measured along y-axis below the principal axis are negative.
Convex lens has positive focal length and concave lens has negative focal length.
Definition
Ray diagram of conventional rays used for image formation in spherical lenses
- A ray emanating from the object parallel to the principal axis of the lens after refraction passes through the second principal focus F (in a convex lens) or appears to diverge (in a concave lens) from the first principal focus F.
- A ray of light, passing through the optical centre of the lens, emerges without any deviation after refraction.
- A ray of light passing through the first principal focus (for a convex lens) or appearing to meet at it (for a concave lens) emerges parallel to the principal axis after refraction.
Diagram
Refraction of rays at spherical surfaces
Definition
Real and virtual images
Real image is formed by the actual intersection of light rays. It can be obtained on a screen. Hence, projectors form real images.
Virtual image is formed when the light rays appear to be originating from a point but does not actually meet. It can be seen by human eyes. Simple microscope forms virtual images.
Note: Concave lens always form virtual images. Convex lens may or may not form virtual images.
Virtual image is formed when the light rays appear to be originating from a point but does not actually meet. It can be seen by human eyes. Simple microscope forms virtual images.
Note: Concave lens always form virtual images. Convex lens may or may not form virtual images.
Example
Effect of image formation when a part of lens is covered or removed
A thin lens has focal length , and its aperture has diameter . If the central part of the aperture, of diameter is blocked by an opaque paper, the focal length of the lens and the intesity of image will become:Intensity of image will depend on the amount of light, which will depend on the area allowing light to enter.
If diameter d/2 is blocked then area gets blocked.
So intensity reduces to as intensity is blocked. The focal length is not affected as the curvature of the lens surfaces are not influenced.
If diameter d/2 is blocked then area gets blocked.
So intensity reduces to as intensity is blocked. The focal length is not affected as the curvature of the lens surfaces are not influenced.
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