Two convex lenses have focal lengths of 50 cm and 25 cm, respectively. If these two lenses are placed in contact, then the net power of this combination will be equal to
- A.+2 dioptre
- B.+6 dioptre
- C.-6 dioptre
- D.+3 dioptre
Correct answer
Explanation
The correct answer is B, +6 dioptre. For lenses in contact the powers simply add, and here they are +2 D and +4 D.
The power of a lens is the reciprocal of its focal length in metres, P = 1/f, and its unit is the dioptre. A convex lens has a positive focal length and therefore positive power. The first lens has f = 50 cm = 0.5 m, so P = 1/0.5 = +2 D. The second lens has f = 25 cm = 0.25 m, so P = 1/0.25 = +4 D. When thin lenses are placed in contact, the net power is the sum of the individual powers: +2 + 4 = +6 D. The combination behaves like a single convex lens of focal length about 16.7 cm.
A is wrong because +2 D is the power of the 50 cm lens alone. C is wrong because two convex lenses give a positive, converging power, not a negative one. D is wrong because +3 D does not follow from adding +2 D and +4 D.
Exam tip: convert focal length to metres before taking 1/f, and add powers for lenses in contact.
Practice Questions
View allThe part of the human eye on which the image is formed is
- A.pupil
- B.cornea
- C.retina
- D.iris
Show answer
The eye lens focuses light on the retina, the light-sensitive layer at the back of the eye, where a real and inverted image is formed.
Read the full explanation →Twinkling of stars is primarily due to the atmospheric
- A.refraction
- B.reflection
- C.polarization
- D.dispersion
Show answer
Starlight is bent again and again as it passes through layers of air whose temperature and density keep changing, so the star seems to flicker in brightness and position.
Read the full explanation →The volume of a sealed packet is 1 litre and its mass is 800 g. The packet is first put inside water with density 1 g cm⁻³ and then in another liquid B with density 1.5 g cm⁻³. Then which one of the following statements holds true?
- A.The packet will float in both water and liquid B.
- B.The packet will sink in both water and liquid B.
- C.The packet will sink in water but will float in liquid B.
- D.The packet will float in water and sink in liquid B.
Show answer
The packet’s density is 800 g divided by 1,000 cm³, which is 0.8 g/cm³, less than the density of both liquids.
Read the full explanation →An object is placed between infinity and the pole (P) of a convex mirror. The position of the image is
- A.between pole (P) and the focus (F), behind the mirror
- B.between the focus (F) and infinity, behind the mirror
- C.between the pole (P) and the infinity, in front of the mirror
- D.at the focus (F), behind the mirror
Show answer
For any position of a real object in front of a convex mirror, the image forms behind the mirror between P and F. A convex mirror bulges outward, and its focus and centre of curvature lie behind it.
Read the full explanation →Light of uniform intensity impinges perpendicularly on a totally reflecting surface. If the area of the surface is halved, the radiation force on it will become
- A.double
- B.half
- C.four times
- D.one fourth
Show answer
The force exerted by light depends on how much light falls on the surface, so with the same intensity, half the area receives half the light and feels half the force.
Read the full explanation →