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The Lens formula is an expression that represents the relationship between the distance of the image (v), the distance of the object (u), and the focal length (f) of the lens.
- A lens is a device that transmits light on the basis of refraction, allowing it to be focused or dispersed into its focal point.
- A lens can be of two types: Concave lens and Convex lens
- If the central portion of the lens is thinner than its edges, it behaves as a divergent lens known as a concave lens.
- If the central portion of a lens is thicker than its edges, then it behaves as a convergent lens, known as a convex lens.
- Lenses are commonly used to correct vision defects in the human eye. Also, they are used in microscopes, telescopes, cameras, projectors, etc.
The Lens formula is given by
1/f = 1/v – 1/u
Where
- f is the focal length of the lens
- u is the distance of the object from the lens
- v is the distance of the image from the lens
Very Short Answers Questions [1 Mark Questions]
Ques. Lens formula relates to
- Image distance
- Object distance
- Focal length
- All of the above
Ans. The correct answer is d. All of the above
Explanation: The lens formula relates the Focal Length of a Lens to the distance between an object in front of it and the image formed by that object.
Ques. The lens formula is given by
- 1/f = 1/u - 1/v
- 1/f = 1/v + 1/u
- 1/f = 2/v - 1/u
- 1/f = 1/v - 1/u
Ans. The correct answer is d. 1/f = 1/v - 1/u
Explanation: The lens formula is given by
1/f = 1/v - 1/u
Where
- f is the focal length of the lens
- u is the distance of the object
- v is the distance of the image
Ques. Which of the following is also known as a diverging lens?
- Concave lens
- Plane mirror
- Convex lens
- Bipolar lens
Ans. The correct answer is a. Concave lens
Explanation: A concave lens is also a diverging lens because it is curved round inwards in the center and bulges outwards at the edges, causing light to diverge.
Ques. Which lens is used in compound microscopes?
- Concave lens
- Convex lens
- Mirror
- Both concave and convex lenses
Ans. The correct answer is b. Convex lenses
Explanation: A compound microscope magnifies an image for an observer by using multiple lenses. It consists of two convex lenses.
Ques. The power of the lens is the reciprocal of its
- Principal axis
- Focal length
- Aperture
- Optical center
Ans. The correct answer is b. Focal length
Explanation: The reciprocal of the focal length of the lens gives the power of the lens.
Short Answers Questions [2 Marks Questions]
Ques. Define lens.
Ans. A lens is a transmissive optical device that employs refraction to focus or disperse a light beam. A simple lens is made up of a single piece of transparent material, whereas a compound lens is made up of multiple simple lenses arranged along a common axis.
Ques. What is the Lens formula?
Ans. The Lens formula expresses the relationship between the distance of the image (v), the distance of the object (u), and the focal length (f) of the lens. The Lens formula applies to both convex and concave lenses. These lenses have negligible thickness.
The lens formula is given by
1/f = 1/v - 1/u
Where
- f is the focal length of the lens
- u is the distance of the object
- v is the distance of the image
Ques. Define the aperture of the lens.
Ans. The aperture is the portion of the lens that is suitable for refraction. The lens's aperture is the effective diameter of its light-transmitting area.
Ques. What are the types of lenses?
Ans. There are two types of lens. They are
- Concave lens: A concave lens diverges a straight light beam from the source to produce a diminished upright virtual image. It can generate both virtual and real images. Concave lenses have at least one curved surface on the interior.
- Convex lens: The convex lens is a lens that converges light rays that are parallel to its principal axis (i.e. converges incoming rays towards the principal axis) and is relatively thick in the center and thin at the lower.
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Long Answers Questions [3 Marks Questions]
Ques. What are the sign conventions of the lens formula?
Ans. Cartesian sign conventions are used to measure the various distances in spherical lens ray diagrams.
- According to the Cartesian sign convention, the object is always positioned on the lens's left side.
- All distances are measured from the lens's optical center.
- Positive distances are measured in the incident light's direction.
- Negative distances are measured in the opposite direction of the incident light.
- Positive distances are those measured vertically and perpendicularly to the principal axis.
- Negative values are assigned to distances measured downward and perpendicular to the principal axis.
Ques. What are the applications of the lens?
Ans. The following are the applications of the lens
- Lenses are used in cameras, telescopes, microscopes, and film projectors.
- Our eyes also have two lenses that allow us to see the world around us.
- Optical instruments such as cameras, glasses, microscopes, telescopes, and projectors require a wide range of lenses.
- Convex lenses in eyeglasses are used to correct farsightedness, which occurs when the distance between the lens of the eye and the retina is too short, causing the focus point to be behind the retina.
- Concave lenses are used in telescopes and binoculars to magnify things.
Ques. An object placed at 50 cm from a lens forms a real image at 80 cm on the other side of the lens. Find its focal length.
Ans. Given
- Distance of the object from the lens, u = - 50 cm
- Distance of the image from the lens, v = 80 cm
From the lens formula, we have
1/f = - 1/u + 1/v
On substituting the values, we get
1/f = - (1/-50) + (1/80)
⇒ f = + 30.8 cm
Therefore the focal length of the lens is 30.8 cm
Very Long Answers Questions [5 Marks Questions]
Ques. Show that the minimum distance between a real object and its real image formed by a lens is equal to 4 times the focal length of the lens.
Ans. For a lens,
- The distance of a real object is taken as negative i.e. -u
- The distance of a real image is taken as positive i.e. +v
L is the distance between the position of the object and its real image from the center of the lens, then
L = |u| + |v| …(i)
We can also above equation as
\(L= (\sqrt{u} - \sqrt{v}^2) + 2\sqrt{uv}\)
Now L will be the minimum if \((\sqrt{u} - \sqrt{v}^2)\) = 0
⇒ u = v …(ii)
From the lens formula, we have
- 1/u + 1/v = 1/f
Using the sign convention and equation (ii), the above equation becomes
- (1/-u) + (1/u) = 1/f
⇒ 2/u = 1/f
⇒ u = 2f
Substituting the above value in equation (i) and using equation (ii), we get
L = 2f + 2f = 4f
The above equation shows that the minimum distance between a real object and its real image formed by a lens is equal to 4 times the focal length of the lens.
Ques. A needle placed 45 cm from a lens forms an image on a screen placed at 90 cm on the other side of the lens. What is the type of lens? Find its focal length. If the length of the needle is 5 cm, what is the length of the image?
Ans. Using the sign convention for a lens, the given data is
- The distance of the needle from the lens, u = - 45 cm
- The distance of the image of the needle from the lens, v = + 90 cm
- Height of the needle, h = 5 cm
From the lens formula, we have
1/f = - 1/u + 1/v
On substituting the values, we get
1/f = - (1/-45) + (1/90)
⇒ f = + 30 cm
Since the focal length is positive, therefore the lens is convex.
Now magnification is given by
m = v/u = h’/h
Where h’ is the height of the image
On substituting the values, we get
(90/-45) = h’/5
⇒ h’ = -10 cm
Hence the length (or height) of the image is 10 cm. The negative sign shows that the image is inverted.
Ques. The image obtained by a convex lens is erect and its length is four times the length of the object. If the focal length of the lens is 20 cm, calculate the object and image distance.
Ans. Let
- h be the size of the object
- u be the distance of the object from the lens
- v be the distance of the image from the lens
Given
- The size of the image, h’ = 4 x size of the object = 4h
- The focal length of the convex lens, f = 20 cm
Magnification produced by the lens is given by
m = v/u = h’/h
On substituting the values, we get
v/u = 4h/h
⇒ v/u = 4
⇒ v = 4u …(i)
From the lens formula, we have
1/f = - 1/u + 1/v
On substituting the values and using equation (i), we get
1/20 = - (1/u) + (1/4u)
⇒ u = -15 cm
From equation (i), v = 4 x (-15) = -60 cm
Hence the object distance is 15 cm and the image distance is 60 cm from the lens. The negative sign in the value of image distance shows that the image is virtual.
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