Question 2 Page 184 - Chapter 10 Class 10 - Light - Reflection and Refraction (Term 1)

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Question 2 Page 184 A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object ? Also, find the power of the lens Given that Image formed is real and of same size, Hence, Magnification = −1 Since Image formed is real, ∴ Image distance is positive Image distance = v = + 50 cm Let the object distance = u We know that, Magnification in a lens = 𝑣/𝑢 −1 = 50/𝑢 ∴ u = 50/(−1) u = − 50 cm ∴ Needle is placed 50 cm infront of the lens Now, In a convex lens Size of image is same as the size of object ∴ Object must be placed at Twice the Focal Length Thus, Object distance = 2 × Focal length 50 = 2 × Focal length Now, In a convex lens Size of image is same as the size of object ∴ Object must be placed at Twice the Focal Length Thus, Object distance = 2 × Focal length 50 = 2 × Focal length Focal length = 50/2 Focal length = 25 cm Focal length = (25 )/100 m Focal length = 0.25 m Now, Power of a lens = 1/(𝐹𝑜𝑐𝑎𝑙 𝐿𝑒𝑛𝑔𝑡ℎ) = 1/0.25 = 100/25 = 4 D ∴ Power of the lens is 4 D