A convex lens of crown glass (μ_g = 1.5) has a focal length of 15 cm. The lens is placed in (a) water (μ_w = 1.33) and (b) carbon bisulphide (μ_c = 1.65). Determine in each case, whether the lens behaves as a converging or diverging lens and determine its focal length.

Solution

Given,
Refractive index of crown glass = 1.5
Focal length of glss = 15 cm
Refractive index of water = 1.33
Refractive index of carbon bisulphide = 1.65

For lens in glass,

\frac{1}{15} = (μ - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})

= (1.5 - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) = 0.5 (\frac{1}{R_{1}} - \frac{1}{R_{2}}) . . . (i)

For lens in water,

\frac{1}{f_{w}} = (\frac{μ_{g} - μ_{w}}{μ_{w}}) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) = (\frac{1.5 - 1.33}{1.33}) (\frac{1}{R_{1}} - \frac{1}{R_{2}}) = \frac{0.17}{1.33} (\frac{1}{R_{1}} - \frac{1}{R_{2}}) . . . (ii)

For lens in carbon bisulphide,

\frac{1}{f_{c}} = (\frac{μ_{g} - μ_{c}}{μ_{c}}) (\frac{1}{R_{1}} - \frac{1}{R_{2}})

= (\frac{1.5 - 1.65}{1.65}) (\frac{1}{R_{1}} - \frac{1}{R_{2}})

= - \frac{0.15}{1.65} (\frac{1}{R_{1}} - \frac{1}{R_{2}})

...(iii)

Dividing (i) by (ii), we get

Focal length of lens when placed in water, f_w = – 58.7 cm.
The positive sign indicates that the lens is converging.

Dividing (i) by (iii), we get
Focal length of lens when placed in carbon bi-sulphide, f_e = – 82.5 cm.
The negative sign indicates that the lens behaves as a diverging lens when it is immersed in carbon bisulphide.

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A convex lens of crown glass (μ_g = 1.5) has a focal length of 15 cm. The lens is placed in (a) water (μ_w = 1.33) and (b) carbon bisulphide (μ_c = 1.65). Determine in each case, whether the lens behaves as a converging or diverging lens and determine its focal length.

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A convex lens of crown glass (μg = 1.5) has a focal length of 15 cm. The lens is placed in (a) water (μw = 1.33) and (b) carbon bisulphide (μc = 1.65). Determine in each case, whether the lens behaves as a converging or diverging lens and determine its focal length.

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A convex lens of crown glass (μ_g = 1.5) has a focal length of 15 cm. The lens is placed in (a) water (μ_w = 1.33) and (b) carbon bisulphide (μ_c = 1.65). Determine in each case, whether the lens behaves as a converging or diverging lens and determine its focal length.