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The relation between focal length 'f', object distance 'u' and image distance 'v' in the case of reflection of light by a spherical mirror is given by ________.
1/f=(uv)/(u+v)
1/f=(1/u)+(1/v)
1/f=(1/u)тИТ(1/v)
1/f=(1/v)тИТ(1/u)
1/f=(1/u)+(1/v)
The relationship between focal length (f), image distance (v), and object distance (u) for spherical mirrors is defined by the mirror formula. It states that the reciprocal of the focal length is equal to the sum of the reciprocal of the image distance and the reciprocal of the object distance.
The relationship between focal length (f), image distance (v), and object distance (u) for spherical mirrors is defined by the mirror formula. It states that the reciprocal of the focal length is equal to the sum of the reciprocal of the image distance and the reciprocal of the object distance.
Think of it as a balance scale where the focus is determined by the combined 'influence' of where you stand (u) and where your reflection appears (v).
Remember 'Mirror is Sum'тАФunlike the lens formula (1/vтИТ1/u=1/f), the mirror formula always has a plus sign.
f1тАЛ=v1тАЛ+u1тАЛ тАФ The Mirror Formula
f=2RтАЛ тАФ Relationship between focal length and radius of curvature
The mirror formula is derived using the properties of similar triangles formed by the object, the image, and the principal axis. It is applicable to both concave and convex mirrors, provided that the sign convention is strictly followed (e.g., measuring distances from the pole).
The formula holds true for all spherical mirrors.
Sign convention: distances measured in the direction of incident light are positive.
The pole of the mirror is taken as the origin (0,0) of the Cartesian coordinate system.
Allows for precise calculation of image position without graphical construction.
Assumes the mirror aperture is small (paraxial rays).
Designing optical instruments like telescopes.
Analyzing image formation in rearview vehicle mirrors.
The focal length (f) is half of the radius of curvature (R).
Option A is mathematically incorrect. Option C and D represent the Lens Formula with swapped variables, which is incorrect for mirrors.
B is correct тАФ The mirror formula relates the reciprocal of the focal length to the sum of the reciprocals of image and object distances.
Always remember the sign convention for competitive exams: 'u' is almost always negative for real objects, and concave mirrors have negative 'f', while convex mirrors have positive 'f'.
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