Sign convention is a set of rules to set signs for image distance, object distance, focal length, etc for mathematical analysis of image formation. Acute angles are positive when produced by anticlockwise rotation from the optic axis, and negative when produced by clockwise rotation. The following sign conventions are used by Cartesian: (1) All distances are measured from the pole of the mirror (in the case of the lens from the optic center). The sign is taken as−(negative) from the pole of a spherical mirror towards the object along the principle axis. An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. (ii) Centre line is shown by DE. Magnification, m = h'h = -vu ∴ Image size, h' = -vhu =-(-54)×(+7)(-27)= -14 cm The image is real, inverted and enlarged in size. (vii) Draw a line CA', backwards, so that it meets the line from D parallel to principal axis at A. https://www.zigya.com/share/U0NFTjEwMDUyOTk3. This sign convention is known as the Cartesian sign convention. (ix) The AB is position of object. As the distances given in the question are large, so we choose a scale of 1: 5, i.e., 1 cm represents 5 cm. This means the sign is always taken as −(negative) in front of a spherical mirror. According to the new Cartesian sign convention for the refraction of light through the concave and convex lens. (vi) Draw a line A'B', perpendicular to principal axis from B'. The heights measured downwards and perpendiculars to the principal axis of the mirror are taken as negative. All the distances in a ray diagram of reflection by spherical mirrors are measured from the pole of the spherical mirror. Delhi - 110058. To measure object distance, image distance, focal length and radius of curvature we need to follow certain sign convention. (5) Heights measured perpendicular to the principal axis, in the downward direction are taken as negative. (xi) Thus the final position, nature and size of the image A'B' are: (a) Position of image A'B' = 3.3 cm × 5 = 16.5 cm from the lens on opposite side. The origin of the Cartesian coordinate system is at the center of the optical component. We draw the ray diagram as follows:(i) Draw the principal axis (a horizontal line). Ltd. Download books and chapters from book store. When we deal with the reflection of light in spherical mirrors, we use a set of sign conventions called the New Cartesian Sign Convention. All distances parallel to the principal axis are measured from the pole of the mirror. Now, using the mirror formula, 1u+1v = 1f∴ 1v = 1f-1u ⇒ = 1-18-1-27 = -3+254 = -154i.e., v = -54 cm The screen should be placed at a distance of 54 cm on the object side of the mirror to obtain a sharp image. 232, Block C-3, Janakpuri, New Delhi, Measure distance BC. Draw the ray diagram and find the position, size and the nature of the image formed. Download the PDF Question Papers Free for off line practice and view the Solutions online. (ix) Now AB', represents the real, but inverted image of the object AB. (c) Height of image A'B': 0.7 × 5 = 3.5 cm, i.e., image is smaller than the object. (b) Nature of image A’B’: Real and inverted. If a virtual image is formed, image is formed on left side, so image distance is negative Since object is always above the principal axis, object height will be positive If image is above the principal axis, image height will be positive. Focal length, f = - 15 cm [f is - ve for a concave lens], Image distance, v = - 10 cm [Concave lens forms virtual image on same side as the object, so v is - ve]. (viii) Draw a line AB, perpendicular (downwards) from A to meet the principal axis at B. Drawing the ray diagram: Using a scale of 1: 5, we get v = - 2 cm, f = - 3 cm. Find the position of the image, its nature and size. We are given a concave mirror. A concave lens of focal length 15 cm forms an image 10 cm from the lens. For example if an image is formed behind the mirror, the distance of image is taken as + (positive) from pole along the principal axis. Sign convention - definition Sign convention is a set of rules to set signs for image distance, object distance, focal length, etc for mathematical analysis of image formation. An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Here, we have Object size, h = + 5 cm Object distance, u = -20 cmRadius of curvature, R = + 3.0 cm [R is +ve for a convex mirror]∴ Focal length , f = R2 = +15 cm From mirror formula, 1v = 1f-1u we have, 1v= 1+15-1-20 = 4+360 = 760 Image distance, v = 607≃ 8.6 cm. (v) Draw a line AD, parallel to principal axis. (iv) Draw an arrow AB of height 1 cm on the left side of lens at a distance of 5 cm from the lens. The pole (P) of the mirror is considered as the origin and the principal axis of the mirror is taken as the x-axis. The height of is taken as + (positive) above the principal axis and taken as – (negative) below the principal axis. This sign convention is known as the Cartesian sign convention. It will be found to be equal to 6 cm.Thus, object is placed at a distance of 6 cm × 5 = 30 cm from the lens.
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