Theory & Procedure, Concave Lens (Focal Length) | Physics Class 12 PDF Download

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Our Objective:

To find the focal length of a concave lens using a convex lens by:

• Lens in contact method
• Lens out of contact method

The Theory:

Concave lens

A concave lens is thinner at the center that at the edges. So the light beams passing through the lens are spread out or diverged. Therefore, the concave lens is called a diverging lens. The image formed by a concave lens is virtual and diminished.
Since a concave lens will not produce a real image, a convex lens is used to measure its focal length. There are two methods to find the focal length of a concave lens.

a) Lens in contact method

When a concave lens of focal length f₂ is placed coaxially in contact with a convex lens of focal length f1 and if F is the focal length of the combination, then,

Therefore, the focal length of the concave lens,

b) Lens out of contact method

The real image (I₁) formed by the convex lens will act as the virtual object for the concave lens. When concave lens is interposed between the convex lens and the real image I₁, the new real image is formed at I₂. If u is the distance of the concave lens from the virtual object I₁ and v is the distance of the concave lens from the real image I₂, then the focal length of the given concave lens is,

Learning outcomes:

• Students list the properties of concave lens.
• Students deduce and apply the lens formula.
• Students identify the two methods used to determine the focal length of concave lens.

Lens in Contact Method

Materials required:

• Illuminated wire gauze
• Lens stand
• Screen
• Metre scale
• A convex lens of short focal length
• Concave lens

Real Lab Procedure:

• Keep the given convex lens of known focal length, f₁, in contact with the concave lens whose focal length to be determined. This forms the combination of lenses.
• It is placed between the illuminated wire gauze and the screen at a fixed distance away from the wire gauze. It is taken as u cm.
• The position of the screen is adjusted to get a clear image of the wire gauze on the screen.
• Measure the distance between the combination of lenses and the screen. It is taken as v cm.
• Calculate the focal length of the combination using the formula:
                                                                                   
• Repeat the experiment by placing the combination of lenses at different distances away from the wire gauze.
• Then calculate the mean value of F.
• Using the values of f1 and F, the focal length of the given concave lens can be calculated using the formula:
  

Observations:

Calculations:

• Focal length of the combination lens, Mean F = …………cm
• Focal length of convex lens, f₁ = ……………cm
• Therefore, the focal length of the given concave lens,  
  

Results:

Focal length of the given concave lens by lens in contact method = …………cm

Lens Out of Contact Method

Materials required:

• Illuminated wire gauze
• Two stands
• Screen
• Metre scale
• A convex lens of short focal length
• Concave lens

Real Lab Procedure:

• The given convex lens is mounted on a stand.
• It is placed between the illuminated wire gauze and the screen at a fixed distance away from the wire gauze.
• The position of the screen is adjusted to get a clear image of the wire gauze on the screen at I₁.
                                 
• Now, the given concave lens (L) is mounted between the screen and the convex lens without any rearrangement.
• The distance between the screen and the concave lens LI₁ is measured as u cm.
• Now, the screen alone is moved back to obtain a clear image I₂ on the screen.
• The distance between the concave lens and the screen, LI₂ is measured as v cm.
  
• Using the values of u and v, the focal length of the concave lens is calculated using the formula, f= uv/u-v.
• To repeat the experiment, remove the concave lens and bring the screen to the initial position. Then place the concave lens at a different position in between the convex lens and screen and record the values in the tabular column.

Observations:

Calculation:

Focal length of concave lens, Mean f = …………….cm

Result:

The focal length of the concave lens by combination method = …………..cm

Simulator Procedure (as performed through the Online Labs)

Select the method from the drop down list.

Select the concave lens from the drop down list.

Lens in Contact

• Select the distance between the lens (combination of convex lens and concave lens) and the object (wire gauze) using the slider.
• To turn On the wire gauze, click on the ‘Light On’ button.
• Adjust the distance between the lens and the screen using the slider to get a clear image of the wire gauze on the screen.
• Note the value of u and v.
• You can calculate the focal length (F) of combination of lenses using the formula F = uv/(u+v).
• The focal length of convex lens (f₁) is shown inside the simulator window.
• You can calculate the focal length of the concave lens using the formula f₂ = (f₁F/(f₁-F).
• You can verify your result by clicking on the ‘Show result’ button.

Lens Out of Contact

• To turn On the wire gauze, click on the ‘Light On’ button.
• Adjust the distance between the convex lens and the screen using the slider to get a clear image of the wire gauze on the screen.
• When a clear image is formed, click on the ‘Insert concave lens’ button to insert the concave lens in between the screen and the convex lens.
• Set the position of the concave lens from the screen using the slider. It is taken as u.
• Adjust the distance between the concave lens and the screen using the slider to get a clear image of the wire gauze on the screen. It is taken as v.
• You can calculate the focal length of the concave lens using the formula f = uv/(u-v).
• You can verify your result by clicking on the ‘Show result’ button.

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