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.

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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.

Given Scenario

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.

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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.

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Questions of 10th Science Chapter 9 in Detail

Define the principal focus of a concave mirror.
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Name a mirror that can give an erect and enlarged image of an object.
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Define 1 dioptre of power of a lens.
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Find the power of a concave lens of focal length 2 m.
We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror?
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An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. What is the position, size and the nature of the image formed.
A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens?
An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image.
The magnification produced by a plane mirror is +1. What does this mean?
An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size.
An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained?
Find the focal length of a lens of power – 2.0 D. What type of lens is this?
A doctor has prescribed a corrective lens of power +1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging?