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Determination of the refractive index of a liquid by pin method using a plane mirror and a convex lens

Theory

Description
 A concave lens cannot form a real image of an object by itself, as it always produces a virtual, erect, and diminished image. Hence, to determine its focal length, an auxiliary convex lens of known focal length is used.

Let a convex lens of known focal length f1 be placed on an optical bench to form a sharp real image of an illuminated object on a screen. If a concave lens is now placed between the convex lens and the screen, the image will become blurred or shift its position as the concave lens diverges the rays.

By moving the concave lens slightly towards or away from the convex lens, a new sharp image is obtained on the screen. The new position of the image gives the combined focal effect of both lenses.

Let f2 be the focal length of the concave lens and f be the equivalent focal length of the combination. Then, from the lens combination formula,

1 ⁄ f = 1 ⁄ f1 + 1 ⁄ f2 —— (1)

Therefore, the focal length of the concave lens is,
1 ⁄ f2 = 1 ⁄ f - 1 ⁄ f1

The equivalent focal length (f) of the combination is obtained experimentally by measuring the object distance (u) and the image distance (v) for the concave lens when used with the convex lens and applying the lens formula,
1 ⁄ f = 1 ⁄ v - 1 ⁄ u.

Finally, the power (P) of the concave lens is given by,
P = 100 ⁄ f (in cm) dioptres.

Thus, by knowing the focal length of the convex lens and the equivalent focal length of the combination, the focal length and power of the concave lens can be accurately determined.

Table & Data Collection

Observation Value
   
   

Calculations & Results

Calculation
 Result:
Focal length of concave lens (f) = cm
Power of concave lens(p) = dioptres

Discussion

Point Explanation
1 A known convex auxiliary lens (with roughly known focal length) was fixed on the optical bench.
2 An object (illuminated pin) and a screen were set so the convex lens produced a sharp real image on the screen; the positions were noted.
3 The concave lens was then placed between the convex lens and the screen (on the same axis) without changing the object position.
4 Inserting the concave lens made the image blur or shift; the concave lens was moved until a sharp image was again formed on the screen.
5 The positions of the object, convex lens, concave lens, and image (screen) were carefully measured and recorded.
6 The concave lens was removed and the original sharp-image position (with only the convex lens) was rechecked to ensure no shift in object or screen.
7 Steps 3-6 were repeated for three sets by slightly changing the object position (e.g., move object back by 5 cm) to get multiple observations.
8 From each set, the object distance (u) and image distance (v) for the concave lens (using sign convention) were calculated and entered in Table-II.
9 The focal length of the concave lens was calculated using the lens formula: 1/f = 1/v - 1/u, and the power was found by P = 100 / f(in cm) diopters.
10 The mean focal length and power were obtained from the three observations and recorded as the final result.