Light from a point source in air falls on a spherical glass surface. If `mu = 1.5`, and radius of curvature `= 20 cm`, the distance of light source from the glass surface is `100 cm` , at what position will the image be formed ? (NCERT Solved Example)
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To solve the problem of finding the position of the image formed by a spherical glass surface when light from a point source in air falls on it, we will use the lens maker's formula and the sign conventions for spherical surfaces.
### Step 1: Identify the given values
- Refractive index of glass, \( \mu = 1.5 \)
- Radius of curvature, \( R = 20 \, \text{cm} \)
- Distance of the light source from the glass surface, \( u = -100 \, \text{cm} \) (the negative sign indicates that the object is on the same side as the incoming light)
### Step 2: Calculate the focal length of the spherical surface
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(i) Device the mathematical n between refractive indices n_(1) and n_(2) of two radii and radius of curvature R for refraction at a convex shperical surface. Consider the object to be a point since lying on the principal axis in rarer medium of refractive index n_(1) and a real image formed in the denser medium of refractive index n_(2) . Hence, derive lens marker's formula. (ii) Light from a point source in air falls on a convex spherical glass surface of refractive index 1.5 and radius of curvature 20cm . The distance of light source from the glass surface is 100cm . At what position is the image formed ?
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