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\(\begin{array}{l}\Rightarrow \end{array} \) \(\begin{array}{l}f = \frac{uv}{u-v}\end{array} \) Ray Diagram Procedure 1. Fix the convex lens in the holder.2. Use the lens to focus an object like a tree on a white screen or a wall. 3. Precisely focus the image of the object on the wall or screen until a sharp image is obtained. 4. Calculate the distance between the lens and the wall or screen. It will be the rough focal length of the lens. 5. Mount the holder with the lens in a locked upright, and place the upright at the 50cm mark. 6. Tune the orientation of the lens in such a way that its surface is perpendicular and vertical to the optical bench’s length. 7. Maintain the upright fixed in the above position throughout.8. Use the thin optical needle as the object (O). Fix it in the outer, laterally movable upright close to zero ends.9. Adjust the object needle upright, and place it at a distance close to 1.5 times the acquired approximate focal length of the lens. 10. Tune the height of the object needle to adjust its tip to lie on the horizontal plane through the lens’s optical centre. Record the position of the index mark on the foot of the object needle upright.11. Close your right eye, and open the left eye. Then watch from the other terminal of the optical bench. The image’s tip should be present in the middle of the lens. 12. Place the thick optical image needle in the fourth upright close to the other terminal of the optical bench. 13. Tune the height of the image needle in a way that its tip is visible in line with the image’s tip when seen with the left eye open. 14. Look towards the right. The tips will be separated. The image needle tip and the image tip have parallax. Clear the parallax tip to tip.15. Record the position of the index mark on the foot of the image needle upright.16. Note down the position of the index mark on the foot of the upright of the lens, the image needle, and the object needle in the second observation column. 17. Calculate the index correction for length between the tip of the object needle and the optical centre of the lens. Next, find the distance between the tip of the image needle and the optical centre of the lens, as mentioned. 18. Adjust the object needle upright towards the mirror in steps 1cm to obtain observations 1 and 2. Repeat the process. 19. Adjust the object needle upright away from the mirror in steps of 1cm to obtain observations 6, 5, and 4. 20. Note down all the observations as shown ahead. Observations The rough or approximate focal length of the convex lens = …….. cm The real length of the index needle x = …….. cm The visible distance between the lens and the object needle when the index needle is positioned between them, y = …….. cm The observed distance between the lens and the image needle when the index needle is positioned between them, z = …….. cm Corrected distance for the object distance ‘u’, x-y = …. cm Corrected distance for the image distance ‘v’, x-z = …. cm Table for u, v; 1/u and 1/v Calculation Calculation of the focal length by the graphical method: 1) u-v Graph Choose a suitable but the same scale to denote v along the Y-axis and u along X-axis. As per sign conventions, v is positive, and u is negative. Plot the points for different rates of v and u from the observation table in the second section. The graph is a rectangular hyperbola, as represented in the graph between u and v. Draw a line OA creating an angle of 45° with either axis bisecting ∠YOX’ and reaching the curve at point A. Draw AC and AB perpendicular on the Y and X’-axis, respectively. The values of v and u are the same for point A. The coordinates of point A should be (2f, 2f), as for a convex lens, when v=2f, u=2f. Therefore, AB = AC = 2f or OB=OC = 2f This implies that f = OB/2 and f = OC/2 Mean value of f = …..cm 2) Choose an apt but the same scale to denote 1/u along the X’-axis and 1/v along the Y-axis. As per sign conventions, 1/u is negative, and 1/v is positive. Plot the points for varied sets of values of 1/u and 1/v from the observation table. The graph evolves to be a straight line as represented in the graph between 1/v and 1/u. The straight-line slices the two-axis OY and OX’ at an angle of 45° at points Q and P, respectively, creating equal intercepts on the axis. Calculate the distance between OQ and OP. Then the focal length, f = 1/OP = 1/ OQ = ……..

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18. Adjust the object needle upright towards the mirror in steps 1cm to obtain observations 1 and 2. Repeat the process. 19. Adjust the object needle upright away from the mirror in steps of 1cm to obtain observations 6, 5, and 4. 20. Note down all the observations as shown ahead.

For a body positioned at a distance ‘u’ from the optical centre of a thin convex lens of focal length ‘f’, an inverted and real image is generated on the lens’s other side at a distance ‘v’ from the optical centre. The relationship between these quantities is:

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The rough or approximate focal length of the convex lens = …….. cm The real length of the index needle x = …….. cm The visible distance between the lens and the object needle when the index needle is positioned between them, y = …….. cm The observed distance between the lens and the image needle when the index needle is positioned between them, z = …….. cm Corrected distance for the object distance ‘u’, x-y = …. cm Corrected distance for the image distance ‘v’, x-z = …. cm

1. Fix the convex lens in the holder.2. Use the lens to focus an object like a tree on a white screen or a wall. 3. Precisely focus the image of the object on the wall or screen until a sharp image is obtained. 4. Calculate the distance between the lens and the wall or screen. It will be the rough focal length of the lens. 5. Mount the holder with the lens in a locked upright, and place the upright at the 50cm mark. 6. Tune the orientation of the lens in such a way that its surface is perpendicular and vertical to the optical bench’s length. 7. Maintain the upright fixed in the above position throughout.8. Use the thin optical needle as the object (O). Fix it in the outer, laterally movable upright close to zero ends.9. Adjust the object needle upright, and place it at a distance close to 1.5 times the acquired approximate focal length of the lens. 10. Tune the height of the object needle to adjust its tip to lie on the horizontal plane through the lens’s optical centre. Record the position of the index mark on the foot of the object needle upright.11. Close your right eye, and open the left eye. Then watch from the other terminal of the optical bench. The image’s tip should be present in the middle of the lens. 12. Place the thick optical image needle in the fourth upright close to the other terminal of the optical bench. 13. Tune the height of the image needle in a way that its tip is visible in line with the image’s tip when seen with the left eye open. 14. Look towards the right. The tips will be separated. The image needle tip and the image tip have parallax. Clear the parallax tip to tip.15. Record the position of the index mark on the foot of the image needle upright.16. Note down the position of the index mark on the foot of the upright of the lens, the image needle, and the object needle in the second observation column. 17. Calculate the index correction for length between the tip of the object needle and the optical centre of the lens. Next, find the distance between the tip of the image needle and the optical centre of the lens, as mentioned.

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2) What is meant by a convex lens? It is an optical lens that usually consists of two spherical surfaces. If the lens is bent outwards, the lens is known as a convex lens.

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a) Tips of the image needle and the object needle must lie at the exact height as the lens’s centre. b) Parallax must be corrected from tip to tip by placing the eye at a distance minimum of 30 cm apart from the needle. c) The object needle must be positioned at such a distance that only an inverted and real image of the object needle is produced. 4) Index correction for u and v must be applied.

You’ll need to be 15 years old to work as a Customer Assistant in most of our stores. However, to work at an airport store you’ll need to be 18 years old or over. There are limits to the hours/days you can work if you’re in school or further education, but this is something we can discuss with you.

3) What is meant by a concave lens? A concave lens is an optical lens that usually consists of two spherical surfaces. If the lens is bent inwards, the lens is known as a concave lens.

2) Choose an apt but the same scale to denote 1/u along the X’-axis and 1/v along the Y-axis. As per sign conventions, 1/u is negative, and 1/v is positive. Plot the points for varied sets of values of 1/u and 1/v from the observation table. The graph evolves to be a straight line as represented in the graph between 1/v and 1/u.

4) What is meant by an optical centre? The optical centre is generally stated as the central point of the given lens, along which a light ray passes without experiencing any deviation.

Create straight lines connecting u3 with u1 with v1, u2 with v2, u3 with v3,………. etc. The lines meet at the intersection point K, as represented in the graph below.

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The straight-line slices the two-axis OY and OX’ at an angle of 45° at points Q and P, respectively, creating equal intercepts on the axis. Calculate the distance between OQ and OP.

If you’re looking for work experience in store, please contact your local store and they may be able to accommodate you. For placements in our Nottingham Support Office you can join our Work Inspiration scheme or send your CV and area of the business you’re interested in to careers@boots.co.uk We will try and support you as much as possible, however, unfortunately we can’t give work experience to everyone.

Calculation of the focal length by the graphical method: 1) u-v Graph Choose a suitable but the same scale to denote v along the Y-axis and u along X-axis. As per sign conventions, v is positive, and u is negative. Plot the points for different rates of v and u from the observation table in the second section. The graph is a rectangular hyperbola, as represented in the graph between u and v.

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Draw a line OA creating an angle of 45° with either axis bisecting ∠YOX’ and reaching the curve at point A. Draw AC and AB perpendicular on the Y and X’-axis, respectively. The values of v and u are the same for point A. The coordinates of point A should be (2f, 2f), as for a convex lens, when v=2f, u=2f.

Choose an apt but the same scale to denote v along the Y-axis and u along the X’-axis. Note the points at distances v1, v2, v3,……. etc., along the OY-axis for various sets of observations from the resulting table.