How Changing Object Distance Affects Image Formation in Physics
Lens Diagram
The lens is a transparent material bounded by two surfaces in which at least one of the surfaces is spherical. It has a principal axis, optical centre, aperture, centre of curvature of lens and principal focus. The two types of lenses are the convex lens and the concave lens. The images formed by these lenses can be real or virtual, depending on various conditions. In this article, we will perform an experiment to observe image distance for different object distances with ray diagrams using a convex lens.
Theory
Convex Lens: A lens which is thin at the edges and thick at the centre is known as a convex lens. This lens converges the light beam incident on it; hence, it is popularly known as a converging lens.
Lens Formula: It is a formula that describes a relationship between object distance and image distance along with focal length. The mathematical representation of this formula is:
1/f= (1/v) - (1/u)
Where v is the distance of the image from the optical centre, f is the focal length of the lens, and u is the distance of the object from the optical centre.
Materials Required
The following materials are essential for the image formation by convex lens experiment.
A convex lens with short focal length (12-20 cm)
Optical bench
A candle
A needle
Measuring Scale
Procedure
Place a lens holder and fix the thin convex lens on it.
Fix the screen on another side of the convex lens and adjust the candle to get an inverted image of the fixed screen, which is clear and sharp. Measure the distance of the candle to get the rough focal length of the lens.
Mark the fixed location of the convex lens as ‘O’.
Now, mark the point F on both sides of the convex lens after calculating the focal length in the first step.
Mark the point 2F on both sides of the convex lens, which is twice the focal length of the convex lens.
Place the candle on the table on the optical bench at beyond 2F distance. Make sure that the height of the flame of the candle must be equal to the centre of the lens by adjusting its height.
Now, adjust the position of the screen to locate a sharp image of the candle flame from another side of the convex lens.
Place the lighted candle at 2F point to record the observations.
Now, shift the object between F and 2F and record the observations. After that, place the object at point F to record the observations.
Place the object between F and O and then record the observations.
Finally, draw the ray diagram for the various positions of the object at which we have recorded the observations.
(Image to be added soon)
The above image shows the ray diagram for different positions of object and image while recording observations.
Observations and Calculations
Case 1: 1/f= (1/v)- (1/u) ⟹ 1/f = 120 - (1/-20) = 2/20 = 1/10 ⟹ f = 10 cm
Case 2: 1/f= (1/v)- (1/u) ⟹ 1/f = 1/30 - (1/-15) = 3/30 = 1/10 ⟹ f = 10 cm
Case 3: 1/f= (1/v)- (1/u) ⟹ 1/f = 1/15 - (1/-30) = 3/30 = 1/10 ⟹ f = 10 cm
Result
FAQs on Image Distance for Varying Object Distances Explained
1. What are object distance (u) and image distance (v) in the context of lenses and mirrors?
In optics, the object distance (u) is defined as the distance from the object to the optical centre of a lens or the pole of a mirror. The image distance (v) is the distance from the image formed to the optical centre of the lens or the pole of the mirror. These two measurements are crucial for determining the properties of an image, such as its size, nature, and location, using the lens or mirror formula.
2. How are object distance, image distance, and focal length related for a thin lens?
The relationship between object distance (u), image distance (v), and focal length (f) for a thin lens is described by the Lens Formula. The formula is: 1/f = 1/v - 1/u. This equation is fundamental in calculating the position of the image when the object distance and the lens's focal length are known. It is essential to use the correct sign conventions for u, v, and f for accurate results.
3. Why is the object distance (u) almost always considered negative in calculations?
The object distance (u) is considered negative based on the Cartesian Sign Convention used in optics. According to this convention:
- Light is assumed to travel from left to right.
- All distances are measured from the optical centre of the lens.
- Distances measured in the same direction as incident light are positive, while distances measured against it are negative.
Since the object is typically placed to the left of the lens (in the path of incoming light), the distance 'u' is measured against the direction of light, making it negative. This ensures calculations are consistent and correctly predict the image's characteristics.
4. How does the image distance (v) of a convex lens change as an object is moved from infinity towards it?
As an object moves from infinity towards a convex lens, the image distance (v) and its nature change systematically:
- Object at infinity: A real, inverted, and point-sized image is formed at the focal point (F) on the other side.
- Object beyond 2F: A real, inverted, and diminished image is formed between F and 2F.
- Object at 2F: A real, inverted image of the same size is formed at 2F.
- Object between F and 2F: A real, inverted, and magnified image is formed beyond 2F.
- Object at F: The image is formed at infinity as the refracted rays become parallel.
- Object between F and the optical centre: A virtual, erect, and magnified image is formed on the same side as the object.
5. If image distance varies for a lens, why does it remain constant in the human eye?
This is a key difference between a rigid lens and the human eye. In the eye, the distance between the eye lens and the retina (where the image is formed) is fixed. Instead of changing the image distance, the eye focuses on objects at different distances by a process called accommodation. The ciliary muscles alter the curvature of the eye lens, which in turn changes its focal length. This adjustment ensures that a sharp image is always formed on the retina, regardless of the object's distance.
6. How does image formation for varying object distances differ between a convex and a concave lens?
The primary difference lies in the type of image formed. A convex lens is a converging lens and can form both real and virtual images depending on the object's position, as described above. In contrast, a concave lens is a diverging lens and always forms a virtual, erect, and diminished image, irrespective of the object's distance from the lens. The image formed by a concave lens is always located between the optical centre and the focus on the same side as the object.
7. What is the importance of drawing ray diagrams when studying image distance?
Ray diagrams are a powerful visual tool that complements the lens formula. Their importance includes:
- Verification: They provide a graphical way to verify the position, size, and nature of an image calculated using the formula.
- Conceptual Understanding: They help in understanding how an image is formed by the intersection of light rays.
- Problem-Solving: For complex systems with multiple lenses, ray tracing can be an intuitive way to approximate the final image location.
By drawing at least two of the three principal rays (a ray parallel to the principal axis, a ray passing through the optical centre, and a ray passing through the principal focus), one can accurately locate the image.
8. What does a negative image distance (v) signify, and can this image be seen?
A negative image distance (v) in lens calculations signifies that the image is virtual and is formed on the same side of the lens as the object. A virtual image is formed where light rays only appear to diverge from. It cannot be projected or captured on a screen because the rays do not actually converge at that point. However, this image can be seen by the human eye, because our eye can trace these diverging rays back to their apparent point of origin, as with a magnifying glass or a concave lens.
