JEE Mains · Physics · STD 12 - 9. Ray optics and optical instruments
The same size images are formed by a convex lens when the object is placed at \(20\, cm\) or at \(10\, cm\) from the lens. The focal length of convex lens is ............ \(cm\).
- A \(10\)
- B \(15\)
- C \(20\)
- D \(30\)
Answer & Solution
Correct Answer
(B) \(15\)
Step-by-step Solution
Detailed explanation
\(m =\frac{ f }{ u + f }\) \(+ m =\frac{ f }{-10+ f } \quad \cdots\) \(- m =\frac{ f }{-20+ f } \ldots\) (1) / (2) \(-1=\frac{ f -20}{ f -10}\) \(10- f = f -20\) \(30=2 f\) \(f =15 cm\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A hanging mass \(M\) is connected to a four times bigger mass by using a string-pulley arrangement. as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by \(2\,Mg\) force. In this situation. tension in the string is \(\frac{x}{5}\) \(Mg\) for \(x =\) Neglect mass of the string and friction of the block (bigger mass) with ice slab. (Given \(g=\) acceleration due to gravity)
JEE Mains 2022 Medium - A ball of mass \(m\) is thrown vertically upward. Another ball of mass \(2\,m\) is thrown an angle \(\theta\) with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is \(\frac{1}{x}\). The value of \(x\) is \(.....\)JEE Mains 2022 Medium
- Two light waves having the same wavelength \(\lambda\) in vacuum are in phase initially. Then the first wave travels a path \(L _{1}\) through a medium of refractive index \(n_{1}\) while the second wave travels a path of length \(L_{2}\) through a medium of refractive index \(n _{2}\). After this the phase difference between the two waves is:JEE Mains 2020 Medium
- In an experiment to determine the period of a simple pendulum of length \(1\, m\), it is attached to different spherical bobs of radii \(r_1\) and \(r_2\) . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be \(5\times10^{-4}\, s\), the difference in radii, \(\left| {{r_1} - {r_2}} \right|\) is best given by .... \(cm\)JEE Mains 2017 Hard
- Figure shows elliptical path \(abcd\) of a planet around the sun \(S\) such that the area of triangle \(csa\) is \(\frac {1}{4}\) the area of the ellipse. (See figure) With \(db\) as the semimajor axis, and \(ca\) as the semiminor axis. If \(t_1\) is the time taken for planet to go over path \(abc\) and \(t_2\) for path taken over \(cda\) then
JEE Mains 2016 Hard - Three masses \(m,\,2\,m\) and \(3\,m\) are moving in \(x-y\) plane with speed \(3\,u,\,2\,u\,\) and \(u\) respectively as shown in figure. The three masses collide at the same point at \(P\) and stick together. The velocity of resulting mass will be
JEE Mains 2014 Hard
More PYQs from JEE Mains
- A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are combined together (without any gap) and this combination has magnification \( m_{1} \), when an object is placed 10 cm before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of 1 cm is introduced between the lenses by moving the concave lens away, which lead to a change in magnification of total lens system to \( m_{2} \).
The value of \(\left|\frac{m_1}{m_2}\right|\) is __________ .JEE Mains 2026 Medium - A man in a car at location \(Q\) on a straight highway is moving with speed \(v\). He decides to reach a point \(P\) in a field at a distance \(d\) from highway (point \(M\) ) as shown in the figure.Speed of the car in the field is half to that on the highway. What should be the distance \(RM\), so that the time taken to reach \(P\) is minimum?
JEE Mains 2018 Hard - The function \(f : R \rightarrow R\) defined by \(f(x)=\lim _{n \rightarrow \infty} \frac{\cos (2 \pi x)-x^{2 n} \sin (x-1)}{1+x^{2 n+1}-x^{2 n}}\) is continuous for all \(x\) in.JEE Mains 2022 Hard
- A cup of coffee cools from \(90^{\circ} \mathrm{C}\) to \(80^{\circ} \mathrm{C}\) in t minutes when the room temperature is \(20^{\circ} \mathrm{C}\). The time taken by the similar cup of coffee to cool from \(80^{\circ} \mathrm{C}\) to \(60^{\circ} \mathrm{C}\) at the same room temperature is :JEE Mains 2025 Medium
- Let \(f: R \rightarrow R\) satisfy \(f(x+y)=2^{x} f(y)+4^{y} f(x), \forall x\), \(y \in R\). If \(f(2)=3\), then \(14 \cdot \frac{f^{\prime}(4)}{f^{\prime}(2)}\) is equal toJEE Mains 2022 Hard
- The value of \(\lim _{n \rightarrow \infty} \frac{[ r ]+[2 r ]+\ldots . .+[ nr ]}{ n ^{2}},\) where
is non-zero real number and \([r]\) denotes the greatest integer less than or equal to \(r\), is equal to ...... .JEE Mains 2021 Hard