Mirror and Lens - To Find Focal Length PDF

 Physics : Experimental skills ® Pre-Medical FOCAL LENGTH OF CONCAVE MIRROR, CONVEX MIRROR...

 Physics : Experimental skills ® Pre-Medical FOCAL LENGTH OF CONCAVE MIRROR, CONVEX MIRROR AND CONVEX LENS Parallax : Fix two needles or nails P and Q vertically on a drawing board or P on a table. View these pins from position A, so that P appears to be directly Q behind Q as shown in fig. Now shift your eye to the left, say to position B. You will observe that the more distant needle P appears to move to the left of Q. Similar observation is there when you shift your eye to the right, say to B A C position C. Thus the object situated at greater distance appears to shift in the same Shows Removal of parallax between P and Q direction as the eye whereas the object situated nearer to the eye, appears to shift in the opposite direction. This apparent shift in the positions of two-objects situated at different distances from the eye, for sideway shift in the position of the eye is called parallax. Parallax may be removed either by moving Q, suitably away from the eye or by moving P towards the eye. When there is no relative shift in the position of P and Q for any position of the eye, then parallax is said to be removed. "No parallax" method or "Removal of parallax" is a very popular method used for tracing or locating the position of the image formed by a mirror or a lens. Introduction of Optical bench : An optical bench consists of a horizontal bed made of wood or metal with a meter scale fixed or fitted along its length. There are three (in some cases four) uprights which can slide along the length of the bed. A sketch of a simple optical bench is shown in figure. Mirror Needle1 Needle2 P [An optical bench] These uprights carry the optical parts like the mirror (or the lens), the object needle, the image needle (or the screen). These uprights are capable of being given a sideway motion ( i.e. perpendicular to the length of the bed) so that the tips of the object and image needle and the centre of mirror (or lens) may be arranged in the same vertical plane. Sharp arrows called the indices are marked on the base of the uprights. These indices help in noting down the positions of the uprights on the scale provided with the bench. Bench error : The variation between the real distance between the point object and the mirror's pole and the recorded distance calculated on optical bench. Bench error = Actual distance – Observed distance. 59 ®  Physics : Experimental skills Pre-Medical EXPERIMENT-1 Objective : To find the value of v for different values of u in case of concave mirror and to find the focal length. Apparatus required : An optical bench along with three uprights, one mirror holder, two needles, given concave mirror etc. uv Formula required : Focal length of a mirror f = u+v M / ///////////////////////////// I C F I' O P u ///// v M' where u = distance of the object from pole and v = distance of the image from pole Procedure : l. Mount the concave mirror in one of the clamp holder such that the principal axis of the mirror is horizontal and parallel to the length of the optical bench. 2. Position the two needles on the uprights and adjust their heights in such a way that the tips of the two needles and the pole of the mirror lie in the same straight line parallel to the length of the optical bench. Mark one pin as object and other image. 3. Bring the object needle towards the pole P of the mirror to a position that lies beyond the focus F but remains between F and C (the centre of curvature of the mirror). Since the object is situated between F and C, so a real and inverted image of the object needle will be formed beyond C as shown. You can see this inverted image in the mirror by closing your one eye and keeping the other eye along the optical bench at the height of the pole of the mirror. 4. Place the second needle on the upright and shift this needle to the position I of the image of the object needle. Remove the parallax between this second needle and the image I of the object needle. In the position of no parallax, the second needle located the position of the image of the object needle. 5. Record the positions of the mirror, the object needle and the image needle on the bench scale and repeat the above steps for five different positions of object needle. Calculations : y 2f 1 (cm-1) u(cm) P O A u O (a) x' x (b) x' 45° 2f Hyperbola curve R 1 (cm-1) Q v (–2f,–2f) v(cm) –1 Scale: x-axis:1division=.....cm Scale: x-axis:1division=.....cm –1 y-axis:1division=.....cm –1 y-axis:1division=.....cm –1 B y' y' 60  Physics : Experimental skills ® Pre-Medical In this graph, at point Q In this graph, focal length 1 1 u = v = 2f f= = OA OB or OP = OR = 2f OP OR ⇒ f= or 2 2 Precautions : 1. All the uprights should be vertical. 2. The tip of the needles and pole of mirror should be at same height. 3. Principle axis of the mirror should be horizontal and parallel to the central line of the optical bench. 4. Parallax of the image and object needles should be removed tip to tip. 5. While removing the parallax, the eye should be kept at a minimum distance of 30 cm from the needle. Sources of error : 1. The uprights may not be vertical. 2. Parallax removal may not be perfect. EXPERIMENT-2 Objective : To find the focal length of a convex mirror using a convex lens. Apparatus required : An optical bench with four uprights, a convex mirror, a convex lens, two needles (an object and an image) etc. Theory : Suppose a convex lens L is kept between a convex mirror M and an object needle O as shown in figure 1. I O C L M [fig-1] r M O L I' [fig-2] When the relative positions of M, L and O are adjusted in such a way that there is no parallax between the object needle O and its image I, then in that position, the rays will fall normally on the convex mirror M. The rays which fall on the mirror normally should meet at the centre of curvature C of the mirror when produced as in figure. The distance MC gives the radius of curvature r. Half of the radius of curvature gives the focal length f of the mirror. Now to get MC, the convex mirror is removed without disturbing the positions of the object O and the lens L and another needle is placed in the position of the image I' of the object O, formed by the lens L as shown in figure 2.. Adjust I' only to remove parallax measure MI'. r MI ' The focal length of convex mirror f = =. 2 2 61 ®  Physics : Experimental skills Pre-Medical Procedure : 1. Mount the concave mirror M, a convex lens L and the object needle O on an optical bench as shown in figure. Look for the inverted image of O through the lens L and the mirror M by adjusting the position of O or L with respect to that of the mirror. When the inverted image is not obtained, a convex lens of larger focal length should be used. 2. Remove the parallax between the object needle O and its inverted image and note the positions of O, L and M on the bench scale. 3. Remove the mirror M and do not disturb the lens L and O at all. Take another needle I' and place it on the other side of the lens. Adjust the position of the needle so that there is no parallax between the needle I' and the inverted image of object needle O formed by the lens. Note this position of the needle I' on the optical bench. 4. Take five sets of observations for different positions of O and L. Precautions : 1. All the uprights should be vertical. 2. The tip of the needle, pole of the mirror and centre of the lens should be at the same height. 3. Principle axis of the lens should be horizontal and parallel to the central of the optical bench. 4. The convex lens should be placed close to the convex lens. 5. Tip to tip parallax should be removed. 6. While removing the parallax, the eye should be kept at a minimum distance of 30 cm from the needle. Sources of error : 1. The uprights may not be vertical. 2. Parallax removal may not be perfect. 3. Focal length of the lens may not be small. EXPERIMENT-3 Object : To find the values of v for different values of u in case of a convex lens and to find its focal length. Apparatus required : An optical bench with three uprights, one lens holder, two needles, given convex lens etc. uv Formula required : Focal length of a lens from lens formula f =. u−v L B' Image of AB 2F A O A' F F 2F C Object needle AB B u v D Ray diagram Procedure : 1. Roughly find the focal length of convex lens by focussing a sharp, clear and inverted image of a distant object on a white paper and measuring this distance between the lens and the white paper with a meter scale. 62  Physics : Experimental skills ® Pre-Medical 2. Level the optical bench, mount the convex lens on the central upright of the optical bench. On the remaining two uprights mount the two needles. Arrange the tips of the needle at the same vertical height as the centre of the lens. 3. One needle AB is object needle and the other one CD is image needle and to make difference between them tip of one of the needles with a piece of chalk or putting a paper flag on it. 4. Shift the position of the object needle AB to a distance greater than 2f from the lens. Look from the other side of the lens along its principal axis near the end of the bench. If the setting is correct, an inverted, real image A'B' is seen. Now adjust the position of the second needle CD such that parallax between the image of the object needle and the image needle is removed. 5. Note the positions of the lense, the object needle and the image needle on the bench scale and thus find the observed values of u and v. 6. Repeat the above steps for 5 different positions of the object by placing it beyond 2 F and between F and 2F. CALCULATION FROM GRAPH : Method-I Method-II Method-III To ∞ y y Scale: x-axis:1division=.....cm–1 Scale x-axis : 1 division =.... cm–1 y v(cm) y-axis:1division=.....cm–1 y-axis : 1 division =.... cm–1 v4 Scale: x-axis:1division=.....cm–1 B y-axis:1division=.....cm–1 Hyperbola v2 v1 v(cm) (–f, f) Q (–2f,–2f) Q R R To ∞ 2f f 1 (cm–1) v 45° x' x 45° x' x u(cm) P O x' x A 1 (cm–1) O u1 u2 u3 u4 P 2f O u 2f y' u(cm) y' y' In this graph In this graph, In this graph, QP QR 1 1 focal length f = or focal length f = –QP = QR focal length f = = 2 2 OA OB Precautions : 1. All the uprights should be vertical. 2. The tip of the needles and centre of lens should be at same height. 3. Principle axis of the lens should be horizontal and parallel to the central line of the optical bench. 4. Parallax of the image and object needles should be removed tip to tip. 5. The object needle should be placed at such a distance that only real, inverted image of it, is formed. Sources of Error : 1. The uprights may not be vertical. 2. Parallax removal may not be perfect. 63