An object AB is placed 15 cm on the left of a convex lens P of focal length 10 cm. Another convex lens Q is now placed 15 cm right of lens P. If the focal length of lens Q is 15 cm, the final image is _____
An object AB is placed 15 cm on the left of a convex lens P of focal length 10 cm. Another convex lens Q is now placed 15 cm right of lens P. If the focal length of lens Q is 15 cm, the final image is _____
- virtual, formed at 7.5 cm right of lens Q, with a size bigger than that of AB
- real, formed at 7.5 cm right of lens Q, with a size same as that of AB
- formed at infinity
- real, formed at 7 cm right of lens Q, with a size smaller than that of AB
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
We analyze image formation by lens \(P\) first. The image formed by lens \(P\) acts as the object for lens \(Q\). The final position and magnification are obtained by applying lens and magnification formulas sequentially.
Step 2: Key Formula or Approach:
Lens formula: \[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \] Magnification: \[ m = \frac{v}{u} \] Total magnification: \[ M = m_1 \times m_2 \]
Step 3: Detailed Explanation:
For Lens \(P\):
\[ u_1 = -15 \text{ cm}, \quad f_1 = +10 \text{ cm} \] \[ \frac{1}{v_1} - \frac{1}{-15} = \frac{1}{10} \Rightarrow \frac{1}{v_1} = \frac{1}{10} - \frac{1}{15} = \frac{1}{30} \] \[ v_1 = +30 \text{ cm} \] Image \(I_1\) is formed 30 cm to the right of lens \(P\).
\[ m_1 = \frac{v_1}{u_1} = \frac{30}{-15} = -2 \]
For Lens \(Q\):
Lens \(Q\) is 15 cm to the right of lens \(P\).
Object distance for \(Q\): \[ u_2 = 30 - 15 = +15 \text{ cm} \] (This is a virtual object for lens \(Q\)).
\[ f_2 = +15 \text{ cm} \] \[ \frac{1}{v_2} - \frac{1}{15} = \frac{1}{15} \Rightarrow \frac{1}{v_2} = \frac{2}{15} \] \[ v_2 = +7.5 \text{ cm} \] Final image is real and formed 7.5 cm to the right of lens \(Q\).
\[ m_2 = \frac{v_2}{u_2} = \frac{7.5}{15} = 0.5 \]
Total Magnification:
\[ M = m_1 \times m_2 = (-2)(0.5) = -1 \] \[ |M| = 1 \] So, the image size is equal to the object size.
Step 4: Final Answer:
The final image is real, formed 7.5 cm to the right of lens \(Q\), and is of the same size as the object.
Top JEE Main Physics Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
Top JEE Main Optics and Refraction Questions
- A spherical surface of radius of curvature \( R \), separates air from glass (refractive index = 1.5). The center of curvature is in the glass medium. A point object \( O \) placed in air on the optic axis of the surface, so that its real image is formed at \( I \) inside glass. The line \( OI \) intersects the spherical surface at \( P \) and \( PO = PI \). The distance \( PO \) equals:
- What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness \( h \) in terms of the angle of incidence \( i \) and angle of refraction \( r \), if the glass slab is placed in air medium?
- Given a thin convex lens (refractive index \( \mu_2 \)), kept in a liquid (refractive index \( \mu_1, \mu_1<\mu_2 \)) having radii of curvature \( |R_1| \) and \( |R_2| \). Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?
- The refractive index of the material of a glass prism is \( 3 \). The angle of minimum deviation is equal to the angle of the prism. What is the angle of the prism?
- For a thin symmetric prism made of glass (refractive index \(1.5\)), the ratio of incident angle and minimum deviation will be _____.
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.