#### To find the image distance for varying object distances in case of a convex lens - Science Practicals

__Aim__

To find the image distance for varying object distances in case of a convex lens and draw corresponding ray diagrams to show the nature of image formed.

__Theory__

The light rays when refracted through a convex lens obey the laws of refraction. The formation of images by a convex lens can be studied by drawing ray diagrams, using the New Cartesian Sign Convention.

In this convention, the optical centre O of a convex lens LL′ is considered as the origin and its principal axis as the x-axis (X′X) of the coordinate system. The principal axis X′X, is an imaginary straight line passing through the two centres of curvature C

_{1}and C

_{2}of the two spherical surfaces of the convex lens LL′. The optical centre O is a point associated with the convex lens such that a ray of light passing through O does not suffer any deviation. Here we consider the convex lens as a thin lens having a small aperture, much less than its radius of curvature.

The new cartesian sign convention can be summarised as below:

(i) The object is always placed to the left of the lens. This implies that the light from the object falls on the lens from the left-hand side.

(ii) All distances parallel to the principal axis are measured from the optical centre of the lens.

(iii) All distances measured to the right of the origin (that is along the +x-axis) are taken as positive while those measured to the left of the origin (that is along (x-axis) are taken as negative.

(iv) Distances measured perpendicular to and above the principal axis (that is along the +y-axis) are taken as positive.

(v) Distances measured perpendicular to and below the principal axis (that is along -y-axis) are taken as negative.

For an illuminated extended object AB of finite size, placed in front of a convex lens, its each small portion acts like a point source of light. An infinite number of rays of light comes from each of these point sources which could be considered for drawing the ray diagrams in order to locate the image of an object formed by a convex lens. For the sake of clarity of ray diagrams, only two rays are considered. These are so chosen as to know their directions easily, after refraction from the convex lens LL′. The intersection of at least two refracted rays gives the position of image of the point object.

Any two of the following rays can be considered for locating the image:

(i) A ray of light from the object, parallel to the principal axis, after refraction from a convex lens, passes through the principal focus F

_{2}on the other side of the lens

_{1}after refraction from a convex lens, will emerge parallel to the principal axis.

(iii) A ray of light passing through the optical centre O of a convex lens will not suffer any deviation

The position of the object may be (a) at infinity, (b) beyond 2F

_{1}, (c) at 2F

_{1}, (d) between F

_{1}and 2F

_{1}, (e) at focus F

_{1}, (f) between focus F

_{1}and optical centre O of the convex lens.

Neat ray diagrams can be drawn for various positions of an object in front of a convex lens, using the New Cartesian Sign Convention and convenient rays for locating the image. It may be considered

that the convex lens is thin and that it has a small aperture. After locating the position of the image, its nature, and size can be determined.

__Materials Required__

Measuring scale, a drawing board, sheets of white paper, protractor, and drawing pins or adhesive tape.

__Procedure__

1. Fix a white sheet of paper on a drawing board. Draw a thin line of about 15 - 18 cm length in the middle of the white sheet.

2. Mark a point O at the centre of this line.

3. Make a convex lens LLabout this point O. Assume O as the optical centre of the lens.

4. Mark points F1 and F2 on either side of the lens such that OF1 = OF2 . (Let F1 and F2 be two principal focii of the lens.) Also mark points 2F1 and 2F2 on the line at double the distances OF1 and OF2.

__Precautions__

1. Use a very sharp tipped pencil to draw thin lines to represent incident and refracted rays.

2. The convex lens drawn should be thin and of small aperture. (This is required for obtaining the distinct image.)

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