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Object And Image Velocity In Plane Mirror - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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6 Questions around this concept.

Solve by difficulty

The $\mathrm{xz}$ - plane separates two media $\mathrm{A}$ and $\mathrm{B}$ with refractive indices $\mathrm{\mu _{1}}$ and $\mathrm{\mu _{2}}$ , respectively. A ray of light travels from $\mathrm{A}$ and $\mathrm{B}$ . Its directions in the two media are given by the unit vectors $\mathrm{r_{A}=a\hat{i}+b\hat{j}}$ and $\mathrm{r_{B}=\alpha \hat{i}+\beta \hat{j}}$ respectively, where $\mathrm{ \hat{i}}$ and $\mathrm{ \hat{j}}$ are unit vectors in the $\mathrm{ x}$ and $\mathrm{y}$ - directions. Then;

$\mu_1 \mathrm{a}=\mu_2 \alpha$

$\mu_1 \alpha=\mu_2^a$

$\mu_1 b=\mu_2 \beta$

None of these

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Concepts Covered - 1

Relation between velocity of object and mirror in plane mirror

The relation between the velocity of the object and mirror in-plane mirror:

In case of plane mirror, distance of the object from the mirror is equal to distance of image from the mirror.

i.e Distance of Image formed in the mirror is same as the distance of the object formed the surface of the mirror.

Hence, from the mirror property:

$$
x_{\mathrm{im}}=-x_{\mathrm{on}}, y_{\mathrm{im}}=y_{\mathrm{om}} \text { and } z_{\mathrm{im}}=z_{\mathrm{om}}
$$

Here $x_{i m}$ means " x coordinate of image with respect to mirror.
Differentiating w.r.t time, we get,

$$
v_{(\mathrm{im}) x}=-v_{(\mathrm{om}) x} ; \quad v_{(\mathrm{im}) y}=v_{(\mathrm{om}) y} ; \quad v_{(\mathrm{im}) \mathrm{z}}=v_{(\mathrm{orn}) z}
$$

Here,
$v_i=$ velocity of the image with respect to the ground.
$v_0=$ velocity of the object with respect to the ground.
$v_{\text {om }}=$ velocity of the object with respect to the mirror.
$v_{i m}=$ velocity of the object with respect to the mirror.
i.e $\vec{v}_{\text {om }}=\vec{v}_{\mathrm{o}}-\vec{v}_{\mathrm{m}} \quad$ and $\quad \vec{v}_{\mathrm{im}}=\vec{v}_{\mathrm{i}}-\vec{v}_{\mathrm{m}}$

For x-axis-

$$
\begin{aligned}
& v_{(i m) x}=-v_{(\mathrm{om}) x} \\
& \Rightarrow \quad v_i-v_{\mathrm{m}}=-\left(v_{\mathrm{o}}-v_{\mathrm{m}}\right) \quad(\text { for } x \text {-axis })
\end{aligned}
$$

- I.e When the object moves with speed $v$ towards (or away) from the plane mirror then image also moves toward (or away) with speed $v$. But the relative speed of image w.r.t. the object is $2 v$.

For y -axis and z -axis

$$
v_{(\mathrm{im}) y}=v_{(\mathrm{om}) y} ; \quad v_{(\mathrm{im}) \mathrm{z}}=v_{(\mathrm{om}) z}
$$

| Relative velocity of image w.r.t. mirror | = | Relative velocity of object w.r.t. mirror |
$\begin{array}{ll}\text { But } & v_1-v_{\mathrm{m}}=\left(v_{\mathrm{o}}-v_{\mathrm{m}}\right) \\ \text { or } & v_{\mathrm{i}}=v_{\mathrm{o}}\end{array} \quad$ for $y$-and $z$-axis.

Here, $v_i=$ velocity of the image with respect to the ground.
$v_0=$ velocity of the object with respect to the ground.

i.e Velocity of the object is equal to the velocity of the image when the object is moving to parallel to the mirror surface.