281948
The ratio of the speed of an object to the speed of its real image of magnification $m$ of a convex mirror is
1 $-\frac{1}{\mathrm{~m}^2}$
2 $\mathrm{m}^2$
3 $-\mathrm{m}$
4 $\frac{1}{\mathrm{~m}}$
Explanation:
A: From mirror formula
$\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{~V}}$
Differentiate above equation with respect to time
$\begin{aligned}
0=\frac{-\mathrm{du}}{\mathrm{dt}} \frac{1}{\mathrm{u}^2}-\frac{1}{\mathrm{v}^2} \frac{\mathrm{dv}}{\mathrm{dt}} \\
\left(\because \frac{\mathrm{du}}{\mathrm{dt}}=\mathrm{u}_{\mathrm{o}} \text { and } \frac{\mathrm{dv}}{\mathrm{dt}}=\mathrm{v}_{\mathrm{o}}\right)
\end{aligned}$
Where, $\mathrm{u}_{\mathrm{o}}$ and $\mathrm{v}_{\mathrm{o}}$ are the velocity of object and image respectively.
$\begin{aligned}
\mathrm{u}_{\mathrm{o}} \frac{1}{\mathrm{u}^2}=-\mathrm{v}_{\mathrm{o}} \frac{1}{\mathrm{v}^2} \\
\frac{\mathrm{u}_{\mathrm{o}}}{\mathrm{v}_{\mathrm{o}}}=-\frac{\mathrm{u}^2}{\mathrm{v}^2} \\
\frac{\mathrm{u}_{\mathrm{o}}}{\mathrm{v}_{\mathrm{o}}}=-\frac{1}{\mathrm{~m}^2}
\end{aligned}$
Manipal UGET-2013
Ray Optics
281949
An object is placed at a distance $20 \mathrm{~cm}$ from the pole of a convex mirror of focal length 20 $\mathrm{cm}$. The image is produced
281950
A ray reflected successively from two plane mirrors inclined at a certain angle undergoes a deviation of $240^{\circ}$. Then, the number of images observable is
1 3
2 5
3 7
4 9
Explanation:
B: Given, angle of deviation $(\delta)=240^{\circ}$ If angle between two plane mirrors $\theta$, Then, Angle of deviation $(\delta)=360^{\circ}-2 \theta$
$\begin{aligned}
240^{\circ}=360^{\circ}-2 \theta \\
2 \theta=360^{\circ}-240^{\circ} \\
2 \theta=120^{\circ} \\
\theta=60^{\circ}
\end{aligned}$
For number of Images observed
$\begin{aligned}
\mathrm{n}=\frac{360^{\circ}}{\theta}-1 \\
\mathrm{n}=\frac{360^{\circ}}{60^{\circ}}-1 \\
\mathrm{n}=5
\end{aligned}$
Manipal UGET-2012
Ray Optics
281951
When a mirror is rotated by an angle $30^{\circ}$, then the reflected ray will be rotated by an angle
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Ray Optics
281948
The ratio of the speed of an object to the speed of its real image of magnification $m$ of a convex mirror is
1 $-\frac{1}{\mathrm{~m}^2}$
2 $\mathrm{m}^2$
3 $-\mathrm{m}$
4 $\frac{1}{\mathrm{~m}}$
Explanation:
A: From mirror formula
$\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{~V}}$
Differentiate above equation with respect to time
$\begin{aligned}
0=\frac{-\mathrm{du}}{\mathrm{dt}} \frac{1}{\mathrm{u}^2}-\frac{1}{\mathrm{v}^2} \frac{\mathrm{dv}}{\mathrm{dt}} \\
\left(\because \frac{\mathrm{du}}{\mathrm{dt}}=\mathrm{u}_{\mathrm{o}} \text { and } \frac{\mathrm{dv}}{\mathrm{dt}}=\mathrm{v}_{\mathrm{o}}\right)
\end{aligned}$
Where, $\mathrm{u}_{\mathrm{o}}$ and $\mathrm{v}_{\mathrm{o}}$ are the velocity of object and image respectively.
$\begin{aligned}
\mathrm{u}_{\mathrm{o}} \frac{1}{\mathrm{u}^2}=-\mathrm{v}_{\mathrm{o}} \frac{1}{\mathrm{v}^2} \\
\frac{\mathrm{u}_{\mathrm{o}}}{\mathrm{v}_{\mathrm{o}}}=-\frac{\mathrm{u}^2}{\mathrm{v}^2} \\
\frac{\mathrm{u}_{\mathrm{o}}}{\mathrm{v}_{\mathrm{o}}}=-\frac{1}{\mathrm{~m}^2}
\end{aligned}$
Manipal UGET-2013
Ray Optics
281949
An object is placed at a distance $20 \mathrm{~cm}$ from the pole of a convex mirror of focal length 20 $\mathrm{cm}$. The image is produced
281950
A ray reflected successively from two plane mirrors inclined at a certain angle undergoes a deviation of $240^{\circ}$. Then, the number of images observable is
1 3
2 5
3 7
4 9
Explanation:
B: Given, angle of deviation $(\delta)=240^{\circ}$ If angle between two plane mirrors $\theta$, Then, Angle of deviation $(\delta)=360^{\circ}-2 \theta$
$\begin{aligned}
240^{\circ}=360^{\circ}-2 \theta \\
2 \theta=360^{\circ}-240^{\circ} \\
2 \theta=120^{\circ} \\
\theta=60^{\circ}
\end{aligned}$
For number of Images observed
$\begin{aligned}
\mathrm{n}=\frac{360^{\circ}}{\theta}-1 \\
\mathrm{n}=\frac{360^{\circ}}{60^{\circ}}-1 \\
\mathrm{n}=5
\end{aligned}$
Manipal UGET-2012
Ray Optics
281951
When a mirror is rotated by an angle $30^{\circ}$, then the reflected ray will be rotated by an angle
281948
The ratio of the speed of an object to the speed of its real image of magnification $m$ of a convex mirror is
1 $-\frac{1}{\mathrm{~m}^2}$
2 $\mathrm{m}^2$
3 $-\mathrm{m}$
4 $\frac{1}{\mathrm{~m}}$
Explanation:
A: From mirror formula
$\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{~V}}$
Differentiate above equation with respect to time
$\begin{aligned}
0=\frac{-\mathrm{du}}{\mathrm{dt}} \frac{1}{\mathrm{u}^2}-\frac{1}{\mathrm{v}^2} \frac{\mathrm{dv}}{\mathrm{dt}} \\
\left(\because \frac{\mathrm{du}}{\mathrm{dt}}=\mathrm{u}_{\mathrm{o}} \text { and } \frac{\mathrm{dv}}{\mathrm{dt}}=\mathrm{v}_{\mathrm{o}}\right)
\end{aligned}$
Where, $\mathrm{u}_{\mathrm{o}}$ and $\mathrm{v}_{\mathrm{o}}$ are the velocity of object and image respectively.
$\begin{aligned}
\mathrm{u}_{\mathrm{o}} \frac{1}{\mathrm{u}^2}=-\mathrm{v}_{\mathrm{o}} \frac{1}{\mathrm{v}^2} \\
\frac{\mathrm{u}_{\mathrm{o}}}{\mathrm{v}_{\mathrm{o}}}=-\frac{\mathrm{u}^2}{\mathrm{v}^2} \\
\frac{\mathrm{u}_{\mathrm{o}}}{\mathrm{v}_{\mathrm{o}}}=-\frac{1}{\mathrm{~m}^2}
\end{aligned}$
Manipal UGET-2013
Ray Optics
281949
An object is placed at a distance $20 \mathrm{~cm}$ from the pole of a convex mirror of focal length 20 $\mathrm{cm}$. The image is produced
281950
A ray reflected successively from two plane mirrors inclined at a certain angle undergoes a deviation of $240^{\circ}$. Then, the number of images observable is
1 3
2 5
3 7
4 9
Explanation:
B: Given, angle of deviation $(\delta)=240^{\circ}$ If angle between two plane mirrors $\theta$, Then, Angle of deviation $(\delta)=360^{\circ}-2 \theta$
$\begin{aligned}
240^{\circ}=360^{\circ}-2 \theta \\
2 \theta=360^{\circ}-240^{\circ} \\
2 \theta=120^{\circ} \\
\theta=60^{\circ}
\end{aligned}$
For number of Images observed
$\begin{aligned}
\mathrm{n}=\frac{360^{\circ}}{\theta}-1 \\
\mathrm{n}=\frac{360^{\circ}}{60^{\circ}}-1 \\
\mathrm{n}=5
\end{aligned}$
Manipal UGET-2012
Ray Optics
281951
When a mirror is rotated by an angle $30^{\circ}$, then the reflected ray will be rotated by an angle
281948
The ratio of the speed of an object to the speed of its real image of magnification $m$ of a convex mirror is
1 $-\frac{1}{\mathrm{~m}^2}$
2 $\mathrm{m}^2$
3 $-\mathrm{m}$
4 $\frac{1}{\mathrm{~m}}$
Explanation:
A: From mirror formula
$\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{u}}+\frac{1}{\mathrm{~V}}$
Differentiate above equation with respect to time
$\begin{aligned}
0=\frac{-\mathrm{du}}{\mathrm{dt}} \frac{1}{\mathrm{u}^2}-\frac{1}{\mathrm{v}^2} \frac{\mathrm{dv}}{\mathrm{dt}} \\
\left(\because \frac{\mathrm{du}}{\mathrm{dt}}=\mathrm{u}_{\mathrm{o}} \text { and } \frac{\mathrm{dv}}{\mathrm{dt}}=\mathrm{v}_{\mathrm{o}}\right)
\end{aligned}$
Where, $\mathrm{u}_{\mathrm{o}}$ and $\mathrm{v}_{\mathrm{o}}$ are the velocity of object and image respectively.
$\begin{aligned}
\mathrm{u}_{\mathrm{o}} \frac{1}{\mathrm{u}^2}=-\mathrm{v}_{\mathrm{o}} \frac{1}{\mathrm{v}^2} \\
\frac{\mathrm{u}_{\mathrm{o}}}{\mathrm{v}_{\mathrm{o}}}=-\frac{\mathrm{u}^2}{\mathrm{v}^2} \\
\frac{\mathrm{u}_{\mathrm{o}}}{\mathrm{v}_{\mathrm{o}}}=-\frac{1}{\mathrm{~m}^2}
\end{aligned}$
Manipal UGET-2013
Ray Optics
281949
An object is placed at a distance $20 \mathrm{~cm}$ from the pole of a convex mirror of focal length 20 $\mathrm{cm}$. The image is produced
281950
A ray reflected successively from two plane mirrors inclined at a certain angle undergoes a deviation of $240^{\circ}$. Then, the number of images observable is
1 3
2 5
3 7
4 9
Explanation:
B: Given, angle of deviation $(\delta)=240^{\circ}$ If angle between two plane mirrors $\theta$, Then, Angle of deviation $(\delta)=360^{\circ}-2 \theta$
$\begin{aligned}
240^{\circ}=360^{\circ}-2 \theta \\
2 \theta=360^{\circ}-240^{\circ} \\
2 \theta=120^{\circ} \\
\theta=60^{\circ}
\end{aligned}$
For number of Images observed
$\begin{aligned}
\mathrm{n}=\frac{360^{\circ}}{\theta}-1 \\
\mathrm{n}=\frac{360^{\circ}}{60^{\circ}}-1 \\
\mathrm{n}=5
\end{aligned}$
Manipal UGET-2012
Ray Optics
281951
When a mirror is rotated by an angle $30^{\circ}$, then the reflected ray will be rotated by an angle