To find the object distance for a concave lens, we use the lens formula: 1/f = 1/v − 1/u, where f is the focal length, v is the image distance, and u is the object distance. For a concave lens, f is -15 cm and v is -10 cm (since it forms a virtual image). Rearranging and solving, 1/−15 = 1/−10 − 1/u, we find u ≈ − 30 cm. The object is placed 30 cm from the lens.
Let’s discuss in detail
Introduction to Lens Formula Application
Understanding Lens Mechanics: The lens formula is a fundamental tool in optics, used to determine the relationship between the object distance, image distance, and focal length of a lens. It is particularly useful in calculating the position of an object or an image formed by lenses.
Concave Lens Characteristics
Nature of a Concave Lens: A concave lens is a diverging lens, meaning it spreads out light rays that pass through it. The focal length of a concave lens is considered negative, as it diverges light rather than converging it.
Image Formation by a Concave Lens: In the provided scenario, a concave lens with a focal length of 15 cm forms an image 10 cm from the lens. Since concave lenses always form virtual images on the same side as the object, the image distance is also negative.
Applying the Lens Formula
Lens Formula Calculation: The lens formula is 1/f = 1/v − 1/u, where f is the focal length, v is the image distance, and u is the object distance. For a concave lens with f = −15 cm and v = −10 cm, this formula can be used to find u.
Calculating Object Distance
Solving for Object Position: Substituting the given values into the lens formula, we get 1/−15 = 1/−10 − 1/u. Solving for u gives us the object distance. The calculation reveals that u is approximately -30 cm.
Result Interpretation: The negative sign indicates that the object is located on the same side of the lens as the light source. Therefore, in this scenario, the object is placed 30 cm from the concave lens. This demonstrates how the lens formula is essential in determining the positions of objects and images in lens systems.