Refractive Index of a Liquid

Materials required:

• The given convex lens
• The given liquid- water
• Plane mirror
• Retort stand
• Pointer
• Mercury
• Meter scale
• China dish

Real Lab Procedure:

To find the focal length of the convex lens:

• The plane mirror is placed horizontally on the base of the retort stand with its reflecting surface upwards.
• The given convex lens is placed over the plane mirror.
• The pointer is arranged horizontally on the clamp of the retort stand, vertically above the lens.
• Looking from above, the height of the pointer is adjusted such that the inverted image of the pointer is obtained.
• The height is further adjusted so that the image coincides with tip of the pointer without parallax. The image and object will be of the same size.
• The distance of the pointer from the top (y1) and bottom (y2) of the lens are measured. The average of these values gives the focal length of the f1 of the convex lens.

$f_{1} =\frac{y_{1}+y_{2}}{2}$

To determine the focal length of the combination of convex lens and liquid lens:

• Remove the lens and place a few drops of the given liquid on the plane mirror.
• The lens is then placed over the liquid with its marked face in contact with the liquid.
• A plano-concave liquid lens is thus formed between the convex lens and the plane mirror.
• The pointer adjustment for coincidence is done and the distance from the top (y1) and bottom (y2) of the lens are measured.
• The average of the two values gives the focal length of the combination, F.

$F =\frac{y_{1}+y_{2}}{2}$

• Then calculate the focal length of the liquid lens using the formula,

$f_{2} = \frac{Ff_{1}}{f_{1}-F}$ To determine the radii of curvature of the lens:

• The convex lens is floated in mercury and taken in a china dish with its marked face in contact with mercury.
• The pointer adjustment for coincidence is done and the distance from the top, d1  of the lens is measured.
• The distance d of the pointer from the centre of the lens is calculated using the formula,

$d=d_{1}\;+\;\frac{y_{2}-y_{1}}{2}$

• Where y2 - y1 is the thickness of the lens.
• Then calculate the radius of curvature of the lens using the formula,

$R=\frac{f_{1}d}{f_{1}-d}$

• So the refractive index of the given liquid can be calculated used using the formula,

$n_{l}=1\;+\;\frac{R}{f_{2}}$

Simulator Procedure (as performed through the Online Labs)

Select the convex lens from the drop down list.

Select the method from the drop down list.

Without Liquid

• Select the distance of the pointer from the bottom of the lens using the slider (Object pointer).
• You can see that the size of the image varies with distance.
• Adjust the pointer so that the image coincides with the tip of the object without parallax. At this stage, the image and object will be of the same size.
• You can see the zoomed view of the object (left) and image (right) on the right side.
• You can view the object and image from different angles of view (left, centre and right) using the slider.
• Measure the height of the pointer from the bottom of the lens. It is taken as y2 cm.
• The thickness of the lens is t cm.
• You can calculate the distance of the pointer from the top of the lens (y1) using the equation, y1 = (y2 -t) cm.
• You can calculate the focal length (f1) of the convex lens using the equation,

$f_{1} =\frac{y_{1}+y_{2}}{2}$

• You can verify your result by clicking on the “Show result’ button.

With Liquid

• Select the liquid from the drop down list.
• Select the distance of the pointer from the bottom of the lens using the slider (Object pointer).
• You can see that the size of the image varies with the distance.
• Adjust the pointer so that the image coincides with the tip of the object without parallax. At this stage, the image and object will be of the same size.
• You can see the zoomed view of the object (left) and image (right) on the right side.
• You can view the object and image from different angles of view (left, centre and right) using the slider.
• Measure the height of the pointer from the bottom of the lens. It is taken as y2 cm.
• The thickness of the lens is fixed as t cm.
• You can calculate the distance of the pointer from the top of the lens (y1) using the equation, y1 = (y2 -t) cm.
• You can calculate the focal length (F) of the convex lens using the equation,

$F =\frac{y_{1}+y_{2}}{2}$

• You can calculate the focal length of the liquid lens (f2) using the equation,

$f_{2} = \frac{Ff_{1}}{f_{1}-F}$

• The radius of curvature of the lens is R cm.
• You can calculate the refractive index of the liquid using the equation,

$n_{l}=1\;+\;\frac{R}{f_{2}}$

• You can verify your results by clicking on the ‘Show result’ button.

To redo the experiment, click the ‘Reset’ button.

Observations:

 Lens used Distance of the pointer from $\frac{y_{1}+y_{2}}{2}$ cm = 10-2 m Top of the lens Bottom of the lens Trial         1 Trial       2 Mean y1 (cm) Trial         1 Trial        2 Mean y2 (cm) Convex lens on plane mirror f1 = Combination (Convex lens + Liquid lens) F = Convex lens floated on Hg d1 =

Calculations:

Focal length of the liquid lens,

$f_{2} =\frac{Ff_{1}}{f_{1}-F}$ = ----------cm

The distance of the pointer from the centre of the lens

$d=d_{1}\;+\;\frac{y_{2}-y_{1}}{2}$ = ---------------cm

Radius of curvature of the lens,

$R=\frac{f_{1}d}{f_{1}-d}$ = -----------cm
Refractive index of given liquid,

$n_{l}=1\;+\;\frac{R}{f_{2}}$ = --------------

Result:

The refractive index of the given liquid by liquid lens arrangement = ----------------

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