Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Geometrical Optics question

2021 · 26 Feb · Shift 1 · Q49
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Geometrical Optics
  5. /2021 · 26 Feb · Shift 1 · Q49

Geometrical Optics question

2021 · 26 Feb · Shift 1 · Q49

JEE MainPhysicsGeometrical OpticsMCQ+4 / −1
A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length has absolute value | f | = 40 cm. The image of object produced by the mirror is of height 25 cm and has the same orientation of the object. One may conclude from the information :
  1. A
    Image is real, same side of convex mirror.
  2. B
    Image is virtual, opposite side of convex mirror.
  3. C
    Image is virtual, opposite side of concave mirror.
  4. D
    Image is real, same side of concave mirror.
View written solutionFree

Correct answer: B

  1. Given data
  • Object height: ho=100 cmh_o = 100\,\text{cm}ho​=100cm
  • Image height: hi=25 cmh_i = 25\,\text{cm}hi​=25cm
  • Mirror focal length magnitude: ∣f∣=40 cm|f| = 40\,\text{cm}∣f∣=40cm
  • Image has the same orientation as the object.
  1. Use magnification

For mirrors,

m=hiho=−vum = \frac{h_i}{h_o} = -\frac{v}{u}m=ho​hi​​=−uv​

So,

m=25100=14m = \frac{25}{100} = \frac{1}{4}m=10025​=41​

Since the image has the same orientation, magnification is positive:

m=+14m = +\frac{1}{4}m=+41​

A positive magnification means the image is erect.

  1. Interpretation of erect image for mirrors

For a spherical mirror:

  • A real image is inverted, so its magnification is negative.
  • An erect image must therefore be virtual.

So the image is virtual.

  1. Check which mirror can form a diminished erect image

  • A concave mirror forms a virtual image only when the object is between pole and focus, and that virtual image is magnified (∣m∣>1|m|>1∣m∣>1).

  • Here, the image is erect but diminished: ∣m∣=14<1|m| = \frac{1}{4} < 1∣m∣=41​<1 So it cannot be a concave mirror.

  • A convex mirror always forms a virtual, erect, diminished image.

Hence the mirror must be convex.

  1. Location of virtual image in a convex mirror

A virtual image formed by a convex mirror lies behind the mirror, i.e. on the opposite side from the object.

  1. Match with options
  • A: Image is real, same side of convex mirror. ❌ Convex mirror does not form real image for a real object.
  • B: Image is virtual, opposite side of convex mirror. ✅ Correct.
  • C: Image is virtual, opposite side of concave mirror. ❌ Concave mirror’s virtual image is erect but magnified, not diminished.
  • D: Image is real, same side of concave mirror. ❌ Real image would be inverted.

Therefore, the correct option is: B\boxed{\text{B}}B​

PreviousNext

More from Geometrical Optics

  • The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors a, b and c respectively. Then choose the correct relation for these vectors.2021 · MCQ
  • Given below are two statements : one is labeled as Assertion A and the other is labeled as Reason R. Assertion A : For a simple microscope, the angular size of the object equals the angular size of the image. Reason R : Magnification is…2021 · MCQ
  • A point source of light S, placed at a distance 60cm in front of the centre of a plane mirror of width 50 cm, hangs vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 1.2 m from it… Includes diagram2021 · Numerical
  • An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is d1 from C and the distance of the image formed is d2 from C, the radius of curvature of this mirror is :2021 · MCQ
  • Find the distance of the image from object O, formed by the combination of lenses in the figure : Includes diagram2021 · MCQ
  • Curved surfaces of a plano-convex lens of refractive index μ 1 and a plano-concave lens of refractive index μ 2 have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the… Includes diagram2021 · MCQ
  • A prism of refractive index n1 and another prism of refractive index n2 are stuck together (as shown in the figure). n1 and n2 depend on λ, the wavelength of light, according to the relation n1​=1.2+λ210.8×10−14​… Includes diagram2021 · Numerical
  • The expected graphical representation of the variation of angle of deviation 'δ' with angle of incidence 'i' in a prism is :2021 · MCQ