Respuesta :
Answer:
The focal length of the lens in ethyl alcohol is 41.07 cm.
Explanation:
Given that,
Refractive index of glass= 1.500
Refractive index of air= 1.000
Refractive index of ethyl alcohol = 1.360
Focal length = 11.5 cm
We need to calculate the focal length of the lens in ethyl alcohol
Using formula of focal length for glass air system
[tex]\dfrac{1}{f}=(n_{g}-n_{a})(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}})[/tex]
Using formula of focal length for glass ethyl alcohol system
[tex]\dfrac{1}{f'}=(n_{g}-n_{ethyl})(\dfrac{1}{R_{1}}-\dfrac{1}{R_{2}})[/tex]
Divided equation (II) by (I)
[tex]\dfrac{f'}{f}=\dfrac{n_{g}-n_{a}}{n_{g}-n_{ethyl}}[/tex]
Where, [tex]n_{g}[/tex] = refractive index of glass
[tex]n_{a}[/tex] = refractive index of air
[tex]n_{ethyl}[/tex] = refractive index of ethyl
Put the value into the formula
[tex]\dfrac{f'}{11.5}=\dfrac{1.500-1.000}{1.500-1.360}[/tex]
[tex]\dfrac{f'}{11.5}=\dfrac{25}{7}[/tex]
[tex]f'=\dfrac{25}{7}\times11.5[/tex]
[tex]f'=41.07\ cm[/tex]
Hence, The focal length of the lens in ethyl alcohol is 41.07 cm.
