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. Find the position of the image, its nature and size.

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NCERT Question 14 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. Find the position of the image, its nature and size. Since object is always placed above the principal axis Height of the object is always positive Height of the object = h = + 5 cm Since the object is placed in front of the mirror Object distance will be negative Object distance = u = βˆ’20 cm Given Radius of curvature = 30 cm We know that, Focal length = (π‘…π‘Žπ‘‘π‘–π‘’π‘  π‘œπ‘“ π‘π‘’π‘Ÿπ‘£π‘Žπ‘‘π‘’π‘Ÿπ‘’)/2 = 30/2 = 15 cm Since focus of a convex mirror is on the right side The focal length will be positive Focal length = f = + 15 cm Finding position of the image Let the image distance = v Using mirror formula 1/𝑓 = 1/𝑒 + 1/𝑣 1/𝑓 βˆ’ 1/𝑒 = 1/𝑣 1/𝑣 = 1/𝑓 βˆ’ 1/𝑒 1/𝑣 = 1/15 βˆ’ 1/((βˆ’20)) 1/𝑣 = 1/15 + 1/20 1/𝑣 = (4 + 3)/60 1/𝑣 = 7/60 𝑣 = 60/7 cm 𝑣 = + 8.6 cm Thus, Image is produced at a distance of 8.6 cm Positive sign denotes the image is formed behind the mirror. Hence, the image is erect Finding size of image Let the height of the image = h’ We know that, Magnification of a mirror = (βˆ’(πΌπ‘šπ‘Žπ‘”π‘’ π‘‘π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’))/(𝑂𝑏𝑗𝑒𝑐𝑑 π‘‘π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’) = 𝑣/𝑒 Also, Magnification of a mirror = (π»π‘’π‘–π‘”β„Žπ‘‘ π‘œπ‘“ 𝑂𝑏𝑗𝑒𝑐𝑑)/(π»π‘’π‘–π‘”β„Žπ‘‘ π‘œπ‘“ π‘–π‘šπ‘Žπ‘”π‘’) = β„Ž^β€²/β„Ž From (1) and (2), (βˆ’π‘£)/𝑒 = β„Ž^β€²/β„Ž (βˆ’(60/7))/((βˆ’20)) = β„Ž^β€²/5 60/(7 Γ— 20) = β„Ž^β€²/5 β„Ž^β€²/5 = 6/(7 Γ— 2) β„Ž^β€² = (6 Γ— 5)/(7 Γ— 2) β„Ž^β€² = (3 Γ— 5)/7 β„Ž^β€² = 15/7 β„Ž^β€² = 2.2 cm Since height of object is 5 cm ∴ Image produced is diminished And since height is positive, image is erect Therefore, Image is virtual, erect and diminished with size 2.2 cm

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CA Maninder Singh is a Chartered Accountant for the past 13 years and a teacher from the past 17 years. He teaches Science, Economics, Accounting and English at Teachoo