Last updated at Sept. 10, 2019 by Teachoo
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
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There are six possibilities of position of object in the case of convex lens: Convex lens converge parallel rays coming from objet at infinity and a highly diminished - point sized, real and inverted image is formed at principal focus F2. Fig: Object at Infinity Properties of Image: Image is highly diminished, real and inverted.Object at infinity:
A diminished, real and inverted image is formed between principal focus, F2 and centre of curvature, C2 at the opposite side when an object is placed beyond C1 of a convex lens. Fig: Object Beyond 2F Properties of Image: Image is diminished, real and inverted. A same sized, real and inverted image is formed at centre of curvature, C2 when object is placed at centre of curvature, C1 of a convex lens.Object at C
Centre of Curvature
Fig: Object at 2F
Properties of Image: Image is same size as object, real and inverted.
An enlarged, real and inverted image is formed beyond centre of curvature, C2 when an object is placed between centre of curvature, C1 and principal focus, F1 of a convex lens. Fig: Object between 2F and F Properties of Image: Image is enlarged, real and inverted. An infinitely large, real and inverted image is formed at infinity when object is placed at principal focus, F1 of a convex lens. Fig: Object at F Properties of Image: Image is highly enlarged, real and inverted.Object at Focus F1
A virtual, erect and enlarged image is formed at the same side of lens, when an object is placed between principal focus, F1 and optical centre, O of a convex lens. Fig: Object between F and O Properties of Image: Image is enlarged, virtual and erect.Summary of Image Formation
Object at Infinity Image is formed at focus. Image is real, inverted and highly diminished in size. Beyond C Image is formed between F2 and 2F2. Image is real, inverted and smaller than object. Between C and F Image is formed beyond C2 or 2F2. Image is real, inverted and larger than object. At C Image is formed at 2F2 or C2. Image is real, inverted and of same size as object. At F Image is formed at infinity. Image is real, inverted and highly enlarged. Between F and O Image is formed on 2F1. Image is virtual, erect and larger than object.
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