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(B) For refraction at a spherical surface,the formula is $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$.Here,the light travels from gla

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$2\, cm$ to the left of the centre

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(B) For refraction at a spherical surface,the formula is $\frac{\mu_2}{v} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}$.Here,the light travels from glass to air,so $\mu_1 = 1.5$ and $\mu_2 = 1$.The object is at a distance of $1.5\, cm$ to the left of the centre. Since the radius is $5.0\, cm$,the object is at a distance of $5.0 - 1.5 = 3.5\, cm$ from the left surface of the sphere.Taking the left surface as the pole,$u = -3.5\, cm$ and $R = -5.0\, cm$.Substituting these values into the formula:$\frac{1}{v} - \frac{1.5}{-3.5} = \frac{1 - 1.5}{-5.0}$$\frac{1}{v} + \frac{1.5}{3.5} = \frac{-0.5}{-5.0}$$\frac{1}{v} + \frac{3}{7} = \frac{1}{10}$$\frac{1}{v} = \frac{1}{10} - \frac{3}{7} = \frac{7 - 30}{70} = -\frac{23}{70}$$v = -\frac{70}{23} \approx -3.04\, cm$.The negative sign indicates the image is formed to the left of the pole (surface). The distance from the centre is $5.0 - 3.04 = 1.96\, cm \approx 2.0\, cm$ to the left of the centre.

$A$ small object is embedded in a glass sphere $(\mu = 1.5)$ of radius $5.0\, cm$ at a distance $1.5\, cm$ to the left of the centre. Locate the image of the object as seen by an observer standing to the left of the sphere.

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