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An object of 7cm placed 27cm infront of a concave mirror of focal length 18cm what is the image distance

Answer»

GivenFocal length of concave mirror (f)= -18cmConventionally concave mirror and concave lens have negative focal lengths and convex mirror and convex lens have positive focal lengths. The co-ordinate system is taken with respect to the Pole as origin. All distances are measured from the pole and distance measured in the direction of light RAYS are positive and opposite to the direction are considered as negative. Distances above the principal axis are positive and vice-versa. Following these conventionsObject distance (u)= -27cmObject height= 7cmLet IMAGE distance be v cmWe know by mirror formula that1/v + 1/u = 1/f1/v + 1/(-27) = 1/(-18)1/v = 1/(-18) + 1/271/v= (-3+2)/541/v= -1/54v= -54 cmThus, PLACING a screen at a distance of 54 cm from the concave mirror on the same SIDE as object will give us a SHARP and focused image.The magnification will bem= -v/um= -(-54)/(-27)m= -2|m|>1 => enlarged image and the negative sign implies that the image is invertedm can also be written asm= Height of image/ Height of object-2= Height of image/7Height of image= -14cmThus the image has a height of 14 cm and is inverted and present at a distance of 54 cm from the mirror.



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