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Concave and convex lenses – Notes and Questions & Answers

POSITION OF IMAGE IN CASE OF CONCAVE LENS

Position of objectPosition of imageSize of imageNature of image
At infinityAt focus F1Highly diminished, point sizedVirtual and erect
Between infinity and optic centre of the lensBetween focus F1 and optic centre of the lensDiminishedVirtual and erect

POSITION OF IMAGE IN CASE OF CONVEX LENS

Position of object
Position of image
Size of imageNature of image
At infinityAt focus F2Highly diminished, point sizedReal and inverted
Beyond 2F1Between F2 and 2 F2DiminishedReal and inverted
At 2F1At 2F2Same sizeReal and inverted
Between F1 and 2F1Beyond 2F2MagnifiedReal and inverted
At focus F1At infinityinfinitely largeReal and inverted
Between F1 and optic centreSame side as objectMagnifiedVirtual and erect

LENS FORMULA, SIGN CONVENTION, MAGNIFICATION AND POWER OF LENS

Lens Formula for concave and convex lens

Formula is same for concave and convex lens but sign convention has to be used carefully

CONCAVE LENSCONVEX LENS
focal length (f)Negative (-)Positive (+)
Object distance (u)Negative (-) (Always placed in the front)Negative (-) (Always placed in the front)
Image distance (v)Negative (-) (Always forms virtual image)Positive (+) for real image formed behind the lens
Negative (-) for virtual image formed in front of the lens

Use of concave and convex lenses as corrective lenses in eye defects

Myopia – Short sight – light focuses short of retina – diverging Concave lens used.

Hypermetropia – Long sight – light focuses long after retina – converging Convex lens used.

Human eye normal with myopia and Hypermetropia

MULTIPLE CHOICE QUESTIONS AND ANSWERS

  • A ray of light parallel to the principal axis after refraction through a concave lens appears to come from:
    • Answer: focal point
  • A lens can be considered to be made up of a glass slab and ___?
    • Answer: 2 prisms
  • The formula for calculating magnification is?
    • Answer: image height/object height
  • A lens that can form an erect, magnified and virtual image is?
    • Answer: convex
  • A lens that always forms an erect, diminished and virtual image is?
    • Answer: concave
  • How is power of lens related to its focal length?
    • Answer: reciprocal of
  • If one half of a convex lens is covered with black paper, will it produce a complete image?
    • Answer: Yes, less intense
  • If a convex lens (ref. index 1.5) is placed in water(ref. index 1.33) its focal length will?
    • Answer: increase
  • If thickness of a convex lens increases its focal length will?
    • Answer: decrease
  • If the focal length of a lens is negative, the lens is?
    • Answer: concave
  • If the focal length of a lens is positive, the lens is?
    • Answer: convex
  • If magnification of a lens is positive then the image formed is?
    • Answer: erect and virtual
  • If magnification of a lens is negative then the image formed is?
    • Answer: inverted and real
  • If the focal length of a lens is decreased its power will:
    • Answer: increase
  • A ray of light passing through a point on the principal axis goes undeviated. The point is:
    • Answer: optic centre
  • The point at which a convex lens converges all incident rays is called?
    • Answer: focal point
  • The lens present in a human eye is?
    • Answer: convex
  • Which lens is used as a magnifying lens?
    • Answer: convex
  • Which lens is used in a simple microscope?
    • Answer: convex
  • Peephole in the door of house uses which lens?
    • Answer: concave
  • Convex lens diverges a beam of light.
    • Answer: False
  • Concave lens is also known as converging lens.
    • Answer: False
  • The power of a lens is +1.0 D. Its focal length and type is?
    • Answer: +1m, convex
  • The power of a lens is +2.0 D. Its focal length and type is?
    • Answer: +0.5m, convex
  • The power of a lens is -2.0 D. Its focal length and type is?
    • Answer: – 0.5 m concave
  • The power of a concave lens of focal length 20 cm is?
    • Answer: -5D
  • The power of a convex lens of focal length 25 cm is?
    • Answer: +4D
  • The power of a concave lens of focal length 25 cm is?
    • Answer: -4D
  • Which lens is used to correct myopia?
    • Answer: concave
  • Which lens is used to correct hypermetropia?
    • Answer: convex
  • The lens used to correct an eye defect where the image is formed in front of the retina is?
    • Answer: concave
  • The lens used to correct an eye defect where the image is formed behind the retina is?
    • Answer: convex
  • The formula for calculating magnification is?
    • Answer: image dist./object dist.
  • Concave lens has a virtual focus.
    • Answer: True
  • Which lens is used to correct short-sightedness?
    • Answer: concave
  • Which lens is used to correct farsightedness?
    • Answer: convex

NUMERICAL QUESTIONS

  • When an object was placed 15 cm in front of a convex lens its image was formed 15 cm behind it. The focal length of the lens is?
    • Answer: f = +7.5 cm, ( u = -15, v = +15 )
  • When an object was placed 20 cm in front of a convex lens its image was formed 20 cm behind it. The focal length of the lens is?
    • Answer: f = +10 cm, ( u = -20, v = +20)
  • When an object was placed 10 cm in front of a convex lens its image was formed 10 cm behind it. The focal length of the lens is?
    • Answer: f = +5 cm, ( u = -10, v = +10 )
  • When an object was placed 30 cm in front of a convex lens its image was formed 30 cm behind it. The focal length of the lens is?
    • Answer: f = +15 cm, ( u = -30, v = +30 )
  • A 2 cm tall object is placed 15 cm in front of a convex lens of focal length 10 cm. Find the position of image.
    • Answer: v = +30 cm, ( u = -15, f = +10 )
  • If an object is placed at a distance of 12 cm in front of a convex lens of focal length of 8 cm, find the position of the image.
    • Answer: v = +24 cm, (u = -12, f = +8)
  • An object placed 10 cm in front of converging lens forms a real image 15 cm behind it. What is the focal length of the lens?
    • Answer: f = +6 cm, (u = -10, v = +15)
  • An object placed 4.8 cm in front of a converging lens forms a real image 8 cm behind it. What is the focal length of the lens?
    • Answer: f = +3 cm; (u = -4.8, v = +8)
  • A convex lens of focal length 10 cm is placed 15 cm in front of a screen. Find object position to get it’s real image on screen?
    • Answer: u = -30 cm, (v = +15, f = +10 )
  • A convex lens of focal length 4 cm is placed 6 cm in front of a screen. Find object position to get it’s real image on screen?
    • Answer: u = -12 cm, (v = +6 , f = +4 )
  • If a real inverted image is formed 12 cm behind a convex lens with a focal length of 8 cm. Find the position of the object.
    • Answer: u = -24 cm, (v = +12, f = +8 )
  • A convex lens of focal length 20 cm is placed 30 cm in front of a screen. Find object position to get it’s real image on screen?
    • Answer: u = -60 cm, (v = +30, f = +20 )
  • An object is placed 10 cm from a convex lens of focal length 20 cm. Find the position of the image.
    • Answer: v = -20 cm, (u = -10 , f = +20)
  • An object is placed 5 cm from a convex lens of focal length 10 cm. Find the position of the image.
    • Answer: v = -10 cm, (u = -5 , f =  +10)
  •  An object is placed 2.5 cm from a convex lens of focal length 5 cm. Find the position of the image.
    • Answer: v = -5 cm; (u = -2.5 , f = +5)
  • An object is placed 4 cm from a convex lens of focal length 6 cm. Find the position of the image.
    • Answer: v = -12 cm; (u = -4 , f = +6)
  • An object is placed 10 cm from a convex lens of focal length 30 cm. Find the position of the image.
    • Answer: v = -15 cm; (u = -10 , f = +30)
  • An object is placed 7.5 cm from a convex lens of focal length 10 cm. Find the position of the image.
    • Answer: v = -30 cm; (u = -7.5, f = +10)
  • An object is placed 4.5 cm from a convex lens of focal length 6 cm. Find the position of the image.
    • Answer: v = -18 cm; (u = -4.5, f = +6 )
  • An object is placed 15 cm from a convex lens of focal length 20 cm. Find the position of the image.
    • Answer: v = -60 cm; (u = -15 , f = +20)
  • A concave lens has a focal length of 20 cm. At what distance should an object be placed to form an image 15 cm in front of the lens?
    • Answer: u = -60 cm; (v = -15 , f = -20)
  • A concave lens has a focal length of 15 cm. At what distance should an object be placed to form an image 10 cm in front of the lens?
    • Answer: u = -30 cm; (v = -10 , f = -15)
  • An object 60 cm from a concave lens gives a virtual image 20 cm in front of the lens. What is the focal length of the lens?
    • Answer: f = -30 cm; (u = -60, v = -20 )
  • An object is placed 15 cm in front of a concave lens of focal length 10 cm. Find the position of the image.
    • Answer: v = -6 cm; (u = -15, f = -10 )
  • An object 3 cm from a concave lens gives a virtual image 2 cm in front of the lens. What is the focal length of the lens?
    • Answer: f = -6 cm; (u = -3, v = -2 )
  • An object 60 cm from a concave lens gives a virtual image 24 cm in front of the lens. What is the focal length of the lens?
    • Answer: f = -40 cm; (u = -60, v = -24)
  • An object 20 cm from a concave lens gives a virtual image 10 cm in front of the lens. What is the focal length of the lens?
    • Answer: f= -20 cm; (u = -20, v = -10)
  • An object 30 cm from a concave lens gives a virtual image 15 cm in front of the lens. What is the focal length of the lens?
    • Answer: f = -30 cm; (u = -30, v = -15 )
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